Xherdan Shaqiri scored one of the goals of the season as Stoke earned a thrilling win at Everton through Marko Arnautovic's injury-time penalty.
The Potters led through Shaqiri early on and after Romelu Lukaku levelled from eight yards, the Swiss looped a stunning half-volley over Tim Howard.
Lukaku struck again after the break and Gerard Deulofeu tapped Everton ahead.
But Joselu volleyed his first Premier League goal and Arnautovic won it after being brought down by John Stones.
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Shaqiri underlines the wow factor
Arnautovic - impressive himself throughout - will be deemed the match winner, but Shaqiri's strike will capture copious column inches in the aftermath of a win which moves Stoke two places above Everton and into eighth.
An ex-Inter Milan and Bayern Munich forward, summer-signing Shaqiri perhaps symbolises the ambition Mark Hughes' side now have and his first goals for the club will raise hopes of many more to come.
John Hartson was full of praise for Shaqiri's goal on Final Score and you can watch the strike on Match of the Day tonight
Stoke kept eight clean sheets in the 11 league games leading up to this win and although their frugal side went missing at Goodison Park, flair at the other end was on show throughout.
Shaqiri's first from six yards saw the combination of Bojan and Arnautovic craft a sublime team goal, while his second - from a wonderful Bojan pass - saw him reach for the ball and clip it over Tim Howard and into the top corner from 18 yards.
"That is the best goal I have seen this season," said Final Score pundit Garth Crooks. "He knew exactly what he was doing, it is absolutely sublime."
Potters dig out what Everton cannot
Everton had lost just once in eight league games before kick-off but with no back-to-back wins in the league this season, their fans could be forgiven for wishing their side packed the killer punch Stoke mustered on Merseyside.
Xherdan Shaqiri's opener underlined the teamwork Stoke showed throughout, with Marko Arnautovic unselfishly teeing him up
Hughes made no changes to his squad despite a 48-hour turnaround from Saturday's win over Manchester United but the likes of Ibrahim Afellay and Glenn Whelan delivered displays of note, both completing 95% of their passes.
It briefly appeared that substituting Bojan moments before Lukaku pulled a long ball down to fire Everton level at 2-2 would prove key, but after falling behind, Stoke's fresh legs earned their manager a fifth league win in eight games.
Arnautovic delivered a telling cross for Joselu to net his first league goal in English football before picking himself up to slam a penalty down the middle despite slipping before making contact.
It was a fitting reward as no Stoke player completed more sprints than the Austrian's 54 in the game and although Shaqiri's brilliance will overshadow his work ethic, the Potters admirably married graft with quality.
Home failure again for Toffees
Everton's industry and spirit are tough to question after they fought back to lead late on but they will rue the chance to record back-to-back wins in the league for the first time this season.
John Stones conceded the crucial penalty and Everton have now conceded 12 goals in six league games
They had 15 shots and as many crosses but the end result smacks of the inconsistency which continues to hamper their hopes of a push for a top-four spot. The gap to Manchester City in fourth is now nine points.
Will Roberto Martinez regret making four changes to the side which won at Newcastle on Boxing Day? His side lacked the fluency Stoke showed before the break, handing the visitors the half-time initiative.
In Lukaku they now boast the Premier League's joint top scorer with Jamie Vardy on 15, but three wins from nine home matches this season is a damning statistic they must rectify if their final league position is to match their ambitions this season.
Man of the match - Xherdan Shaqiri
Xherdan Shaqiri's second goal of the game will stand out but his lively start also established Stoke's first-half momentum
Manager reaction
Everton manager Roberto Martinez on Stoke's penalty: "Looking at the replay it shows John Stones touches the ball. That decision is hard to take. To get a decision wrong like that so late in the game makes you feel furious and is unacceptable."
Stoke manager Mark Hughes: "The only thing lacking up until today for Shaqiri was goals - performances had been fine - but now he has added that. He has that quality - it's his first mark in terms of goals and I'm sure there will be more to come. It was end to end and I thought both sides came out with great credit."
Up next
Stoke can make it three wins from three if they win at West Bromwich Albion on Saturday while Everton host Tottenham 24 hours later.
Lineup, Bookings (3) & Substitutions (5)
Everton
- 24 Howard
- 23 Coleman
- 05 Stones Booked
- 25 Funes Mori
- 32 Galloway
- 20 Barkley
- 18 Barry
- 16 McCarthy (Naismith - 26' )
- 19 Deulofeu Booked
- 10 Lukaku
- 09 Koné
Substitutes
- 01 Robles
- 03 Baines
- 04 Gibson
- 14 Naismith
- 15 Cleverley (Naismith - 65' )
- 17 Besic
- 21 Osman
Stoke City
- 01 Butland
- 08 Johnson
- 17 Shawcross
- 26 Wollscheid Booked
- 03 Pieters
- 20 Cameron (Walters - 78' )
- 06 Whelan
- 22 Shaqiri (Van Ginkel - 87' )
- 14 Afellay
- 10 Arnautovic
- 27 Krkic (Joselu - 64' )
Substitutes
- 11 Joselu
- 12 Wilson
- 15 Van Ginkel
- 16 Adam
- 18 Diouf
- 19 Walters
- 29 Haugaard
Match Stats
Live Text Commentary
Full Time Match ends, Everton 3, Stoke City 4.
90:00 +3:25 Full timeFull Time Second Half ends, Everton 3, Stoke City 4.
90:00 +2:15Brendan Galloway (Everton) wins a free kick on the left wing.
90:00 +2:15Foul by Joselu (Stoke City).
90:00 +0:32 Goal scoredGoal! Goal! Everton 3, Stoke City 4. Marko Arnautovic (Stoke City) converts the penalty with a right footed shot to the high centre of the goal.
89:40 BookingBooking John Stones (Everton) is shown the yellow card for a bad foul.
89:35Penalty conceded by John Stones (Everton) after a foul in the penalty area.
89:35Penalty Stoke City. Marko Arnautovic draws a foul in the penalty area.
88:51Attempt missed. Seamus Coleman (Everton) left footed shot from the right side of the box is too high.
88:15John Stones (Everton) wins a free kick in the attacking half.
88:15Foul by Marco Van Ginkel (Stoke City).
87:42Offside, Stoke City. Ibrahim Afellay tries a through ball, but Ryan Shawcross is caught offside.
87:12Foul by John Stones (Everton).
87:12Marco Van Ginkel (Stoke City) wins a free kick on the right wing.
86:10 SubstitutionSubstitution Substitution, Stoke City. Marco Van Ginkel replaces Xherdan Shaqiri.
85:44Offside, Stoke City. Ibrahim Afellay tries a through ball, but Jonathan Walters is caught offside.
84:29Offside, Everton. Ross Barkley tries a through ball, but Seamus Coleman is caught offside.
81:26Hand ball by Joselu (Stoke City).
80:48Corner, Everton. Conceded by Philipp Wollscheid.
79:37 Goal scoredGoal! Goal! Everton 3, Stoke City 3. Joselu (Stoke City) right footed shot from the right side of the box to the high centre of the goal.
Foul by Arouna Koné (Everton).
78:39Marko Arnautovic (Stoke City) wins a free kick in the defensive half.
77:58 SubstitutionSubstitution Substitution, Stoke City. Jonathan Walters replaces Geoff Cameron.
76:47Attempt missed. Gerard Deulofeu (Everton) right footed shot from the centre of the box misses to the left.
70:13 Goal scoredGoal! Goal! Everton 3, Stoke City 2. Gerard Deulofeu (Everton) right footed shot from very close range to the centre of the goal. Assisted by Ross Barkley.
68:17Delay over. They are ready to continue.
67:32Corner, Everton. Conceded by Ryan Shawcross.
67:31Attempt blocked. Steven Naismith (Everton) right footed shot from the centre of the box is blocked. Assisted by Romelu Lukaku.
66:21Seamus Coleman (Everton) wins a free kick in the defensive half.
66:21Foul by Marko Arnautovic (Stoke City).
65:00Offside, Stoke City. Marko Arnautovic tries a through ball, but Joselu is caught offside.
64:38 SubstitutionSubstitution Substitution, Everton. Steven Naismith replaces Tom Cleverley.
63:31 Goal scoredGoal! Goal! Everton 2, Stoke City 2. Romelu Lukaku (Everton) right footed shot from the centre of the box to the bottom left corner. Assisted by Tom Cleverley.
63:02 SubstitutionSubstitution Substitution, Stoke City. Joselu replaces Bojan.
62:12Attempt missed. Arouna Koné (Everton) right footed shot from outside the box is too high. Assisted by Tom Cleverley.
57:50Attempt blocked. Ross Barkley (Everton) right footed shot from the right side of the box is blocked. Assisted by Gerard Deulofeu.
56:58Attempt saved. Geoff Cameron (Stoke City) right footed shot from outside the box is saved in the centre of the goal. Assisted by Erik Pieters.
54:21Foul by Marko Arnautovic (Stoke City).
54:21Gerard Deulofeu (Everton) wins a free kick in the attacking half.
52:19Foul by Marko Arnautovic (Stoke City).
52:19Tim Howard (Everton) wins a free kick in the defensive half.
51:50Corner, Stoke City. Conceded by Ramiro Funes Mori.
48:30Foul by Xherdan Shaqiri (Stoke City).
48:30Brendan Galloway (Everton) wins a free kick on the left wing.
47:46Corner, Everton. Conceded by Glen Johnson.
47:42Attempt blocked. Tom Cleverley (Everton) left footed shot from the centre of the box is blocked. Assisted by Romelu Lukaku.
46:31Ibrahim Afellay (Stoke City) wins a free kick in the defensive half.
46:31Foul by Gareth Barry (Everton).
45:00Second Half begins Everton 1, Stoke City 2.
45:00 +2:10 Half timeHalf Time First Half ends, Everton 1, Stoke City 2.
45:00 +1:47Bojan (Stoke City) wins a free kick in the defensive half.
45:00 +1:47Foul by Seamus Coleman (Everton).
44:26 Goal scoredGoal! Goal! Everton 1, Stoke City 2. Xherdan Shaqiri (Stoke City) right footed shot from the right side of the box to the top left corner. Assisted by Bojan with a through ball.
43:33Offside, Stoke City. Xherdan Shaqiri tries a through ball, but Marko Arnautovic is caught offside.
42:07Bojan (Stoke City) wins a free kick in the attacking half.
42:07Foul by John Stones (Everton).
41:40Xherdan Shaqiri (Stoke City) wins a free kick in the defensive half.
41:40Foul by Arouna Koné (Everton).
39:45 BookingBooking Gerard Deulofeu (Everton) is shown the yellow card.
39:35Gerard Deulofeu (Everton) has gone down, but that's a dive.
38:29Attempt blocked. Ross Barkley (Everton) right footed shot from the left side of the box is blocked. Assisted by Romelu Lukaku with a headed pass.
38:02Attempt blocked. Arouna Koné (Everton) left footed shot from outside the box is blocked. Assisted by Gerard Deulofeu.
33:09Bojan (Stoke City) wins a free kick in the defensive half.
33:09Foul by Gareth Barry (Everton).
31:08Attempt missed. Brendan Galloway (Everton) left footed shot from outside the box is close, but misses to the right. Assisted by Ross Barkley.
28:14Foul by Tom Cleverley (Everton).
28:14Ibrahim Afellay (Stoke City) wins a free kick in the defensive half.
27:40Corner, Everton. Conceded by Ryan Shawcross.
26:32Offside, Everton. Romelu Lukaku tries a through ball, but Arouna Koné is caught offside.
25:45 SubstitutionSubstitution Substitution, Everton. Tom Cleverley replaces James McCarthy because of an injury.
24:44Attempt blocked. Geoff Cameron (Stoke City) left footed shot from the centre of the box is blocked.
24:13Corner, Stoke City. Conceded by Ramiro Funes Mori.
23:00 BookingBooking Philipp Wollscheid (Stoke City) is shown the yellow card for a bad foul.
22:54Foul by Philipp Wollscheid (Stoke City).
22:54Romelu Lukaku (Everton) wins a free kick in the defensive half.
21:36 Goal scoredGoal! Goal! Everton 1, Stoke City 1. Romelu Lukaku (Everton) left footed shot from the centre of the box to the bottom left corner. Assisted by James McCarthy with a through ball.
17:40Attempt missed. John Stones (Everton) header from the centre of the box misses to the left. Assisted by Gareth Barry with a cross following a corner.
17:18Corner, Everton. Conceded by Philipp Wollscheid.
15:53 Goal scoredGoal! Goal! Everton 0, Stoke City 1. Xherdan Shaqiri (Stoke City) left footed shot from the centre of the box to the bottom right corner. Assisted by Marko Arnautovic.
12:41Attempt missed. Romelu Lukaku (Everton) left footed shot from outside the box is too high. Assisted by James McCarthy.
11:53Hand ball by Erik Pieters (Stoke City).
11:26Attempt missed. Marko Arnautovic (Stoke City) right footed shot from the right side of the box is close, but misses to the left. Assisted by Bojan.
10:19Foul by Erik Pieters (Stoke City).
10:19Gerard Deulofeu (Everton) wins a free kick on the right wing.
9:36Corner, Everton. Conceded by Glenn Whelan.
9:35Attempt blocked. Ross Barkley (Everton) right footed shot from outside the box is blocked. Assisted by Brendan Galloway.
8:38Foul by Geoff Cameron (Stoke City).
8:38Ross Barkley (Everton) wins a free kick in the attacking half.
8:04Offside, Stoke City. Xherdan Shaqiri tries a through ball, but Marko Arnautovic is caught offside.
6:56Delay over. They are ready to continue.
6:12Delay in match Philipp Wollscheid (Stoke City) because of an injury.
0:51Foul by Ibrahim Afellay (Stoke City).
0:51James McCarthy (Everton) wins a free kick in the defensive half.
0:42Attempt blocked. Marko Arnautovic (Stoke City) right footed shot from outside the box is blocked. Assisted by Xherdan Shaqiri.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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