Romelu Lukaku scored his sixth goal in five league games to equalise with a late strike in an entertaining match against Crystal Palace.
Poor Everton defending allowed Scott Dann to head Palace in front late on as the Londoners looked on course to win.
But Lukaku - who had twice struck the woodwork - tapped in Gerard Deulofeu's low cross from two yards for a deserved point for the dominant hosts.
Palace's Jordon Mutch sent a shot wide as both sides searched for a winner.
The draw was still enough to move Palace to sixth on goal difference, though manager Alan Pardew will be disappointed that his team only held their lead for five minutes, to drop points from a winning position for the first time this season.
But Everton dominated possession and, in the second half in particular, were adventurous and easy on the eye.
Read reaction from the draw between Everton and Palace.
Everton boss Roberto Martinez has boasted he has some of the most valuable young talent in Europe at his disposal and the Spaniard's highly-prised quartet strengthened the manager's claim with their performances against Palace.
Record signing Lukaku, Ross Barkley, John Stones and Gerard Deulofeu - aged 22, 22, 21 and 21 respectively - were authoritative and influential, as they have been all season.
Lukaku's power posed Palace problems, with the post denying him a first-half goal and the crossbar stopping him from equalising straight after Palace took the lead.
Barkley and Deulofeu were inventive, with the latter's sublime second-half free-kick forcing Connor Wickham to head a defensive header onto his own crossbar, while it was former Barcelona prodigy Deulofeu who again provided the assist to his ruthless team-mate.
At the back, Stones anticipated play brilliantly and, as has become routine this campaign, had the confidence and guile to glide out of defence and even pose a threat in the final third - a quick turn in the box followed up by a dangerous cross was a particular highlight.
Martinez has said a Champions League place is the club's aim this season and he certainly has four players who, on current form, would be at ease facing Europe's elite.
Only Jamie Vardy, the Premier League's top scorer with 14, has scored more league goals than the £28m Lukaku, while he is on course to become the first Everton striker to score more than 20 league goals since Gary Lineker in 1985-86
The Belgian has consistently been a threat, missing only 39 minutes of action this campaign, and was a menace against Palace before levelling with his 50th goal in a century of Everton appearances.
Martinez describe his striker as sensational, adding: "He is always there to give us a focal point and score goals.
"It was a big moment. One hundred games is a landmark and 50 goals is a remarkable return. He is in a very good moment of his career. He is vital in everything we are trying to do."
Palace have already picked up more points away from home than at Selhurst Park this season and, having thrashed Newcastle 5-1 at home in their previous league outing, are a team in form.
But their sporadic attacks mainly came on the counter-attack against Everton and a Wickham header at the near post, which forced a fine save from Tim Howard, was the closest they came to scoring before Dann gave his team the lead against the run of play.
It had been all Everton after the break before the defender got the better of the static Gareth Barry and Arouna Kone at a corner to score with a simple header, for his second goal at Goodison in three seasons.
But Palace must be praised for holding firm when under pressure, with such stoicism illustrating why they have been successful on the road. Since Pardew took charge in January, the Eagles have collected 31 points away from home with only Arsenal of the Premier League's clubs amassing more.
Palace argued for a penalty when Barry tugged on Mile Jedinak's shirt, but Pardew believed a draw was a fair result.
"If we could have seen that five minutes out after our goal, it might have been different, but all credit to Everton - they kept coming and we are really pleased with a draw as it takes us sixth and with a home game to come," said the Eagles boss.
Everton, unbeaten in seven games, will be confident of extending their run should they continue to perform with such assurance against their next three opponents - Norwich (away on Saturday at 12:45 GMT), Leicester (home) and Newcastle (away). Crystal Palace, meanwhile, host Southampton on Saturday (15:00 GMT) before travelling to Stoke.
Full Time Match ends, Everton 1, Crystal Palace 1.
90:00 +3:25 Full timeFull Time Second Half ends, Everton 1, Crystal Palace 1.
90:00 +3:12Attempt blocked. Arouna Koné (Everton) right footed shot from the centre of the box is blocked. Assisted by Tom Cleverley.
90:00 +0:28Attempt missed. Jordon Mutch (Crystal Palace) left footed shot from outside the box misses to the right.
89:40Attempt blocked. Tom Cleverley (Everton) left footed shot from outside the box is blocked.
89:36Attempt missed. Ross Barkley (Everton) left footed shot from outside the box misses to the right.
88:51Offside, Crystal Palace. Jordon Mutch tries a through ball, but Yannick Bolasie is caught offside.
87:36 BookingBooking Ramiro Funes Mori (Everton) is shown the yellow card for a bad foul.
87:25Foul by Ramiro Funes Mori (Everton).
87:25Yannick Bolasie (Crystal Palace) wins a free kick on the left wing.
86:27 BookingBooking James McArthur (Crystal Palace) is shown the yellow card for a bad foul.
86:22Tom Cleverley (Everton) wins a free kick in the defensive half.
86:22Foul by James McArthur (Crystal Palace).
85:04Attempt blocked. Yannick Bolasie (Crystal Palace) left footed shot from the right side of the box is blocked.
83:07Offside, Crystal Palace. Pape Souaré tries a through ball, but Yannick Bolasie is caught offside.
82:20Romelu Lukaku (Everton) wins a free kick in the defensive half.
82:20Foul by Joel Ward (Crystal Palace).
81:40Foul by Seamus Coleman (Everton).
81:40Dwight Gayle (Crystal Palace) wins a free kick on the left wing.
80:43 Goal scoredGoal! Goal! Everton 1, Crystal Palace 1. Romelu Lukaku (Everton) right footed shot from very close range to the centre of the goal. Assisted by Gareth Barry.
Corner, Everton. Conceded by Damien Delaney.
77:54Romelu Lukaku (Everton) hits the bar with a left footed shot from outside the box. Assisted by Gareth Barry.
76:59 SubstitutionSubstitution Substitution, Crystal Palace. Jordon Mutch replaces Yohan Cabaye.
76:48 SubstitutionSubstitution Substitution, Crystal Palace. Dwight Gayle replaces Connor Wickham.
75:32 Goal scoredGoal! Goal! Everton 0, Crystal Palace 1. Scott Dann (Crystal Palace) header from the centre of the box to the centre of the goal. Assisted by Jason Puncheon with a cross following a corner.
74:47Corner, Crystal Palace. Conceded by Tim Howard.
74:46Attempt saved. Jason Puncheon (Crystal Palace) left footed shot from the centre of the box is saved in the top right corner.
69:56Corner, Everton. Conceded by Mile Jedinak.
69:32Corner, Everton. Conceded by Damien Delaney.
68:59Corner, Everton. Conceded by Wayne Hennessey.
68:10Attempt saved. Tom Cleverley (Everton) right footed shot from outside the box is saved in the centre of the goal. Assisted by Gerard Deulofeu.
65:36Attempt blocked. Ross Barkley (Everton) right footed shot from outside the box is blocked.
65:04Corner, Everton. Conceded by Wayne Hennessey.
65:03Attempt saved. Tom Cleverley (Everton) right footed shot from outside the box is saved in the top centre of the goal.
61:58 SubstitutionSubstitution Substitution, Everton. Leighton Baines replaces Brendan Galloway.
61:24Attempt missed. Damien Delaney (Crystal Palace) right footed shot from the centre of the box misses to the right. Assisted by Jason Puncheon with a cross following a corner.
60:47Corner, Crystal Palace. Conceded by Brendan Galloway.
60:14Attempt blocked. Ross Barkley (Everton) left footed shot from outside the box is blocked. Assisted by Gareth Barry.
58:41Brendan Galloway (Everton) wins a free kick on the left wing.
58:41Foul by Joel Ward (Crystal Palace).
58:14John Stones (Everton) wins a free kick in the defensive half.
58:14Foul by Connor Wickham (Crystal Palace).
57:08Corner, Everton. Conceded by Damien Delaney.
55:34Corner, Everton. Conceded by Pape Souaré.
54:49Attempt saved. Yannick Bolasie (Crystal Palace) left footed shot from the left side of the box is saved in the bottom right corner. Assisted by Jason Puncheon.
54:08Ross Barkley (Everton) wins a free kick in the defensive half.
54:08Foul by Mile Jedinak (Crystal Palace).
52:54 BookingBooking Connor Wickham (Crystal Palace) is shown the yellow card for a bad foul.
52:50John Stones (Everton) wins a free kick in the defensive half.
52:50Foul by Connor Wickham (Crystal Palace).
52:11Attempt missed. Ross Barkley (Everton) header from the centre of the box is close, but misses to the right. Assisted by Arouna Koné with a cross.
51:11Corner, Crystal Palace. Conceded by Seamus Coleman.
50:34Tim Howard (Everton) wins a free kick in the defensive half.
50:34Foul by Connor Wickham (Crystal Palace).
50:30Attempt missed. Mile Jedinak (Crystal Palace) header from the centre of the box is close, but misses to the left. Assisted by Jason Puncheon with a cross following a corner.
49:58Corner, Crystal Palace. Conceded by Ramiro Funes Mori.
49:18Foul by Arouna Koné (Everton).
49:18Joel Ward (Crystal Palace) wins a free kick in the defensive half.
48:58Gerard Deulofeu (Everton) wins a free kick in the defensive half.
48:58Foul by Mile Jedinak (Crystal Palace).
48:13Attempt missed. Arouna Koné (Everton) right footed shot from outside the box is high and wide to the right. Assisted by Romelu Lukaku.
46:23Corner, Everton. Conceded by Yohan Cabaye.
45:47Corner, Everton. Conceded by Mile Jedinak.
45:00Second Half begins Everton 0, Crystal Palace 0.
45:00 +1:04 Half timeHalf Time First Half ends, Everton 0, Crystal Palace 0.
44:23Attempt missed. Yohan Cabaye (Crystal Palace) right footed shot from outside the box misses to the right. Assisted by James McArthur.
43:25Attempt saved. Gareth Barry (Everton) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by John Stones.
42:57Corner, Everton. Conceded by Connor Wickham.
42:56Attempt blocked. Romelu Lukaku (Everton) left footed shot from a difficult angle on the left is blocked. Assisted by Gareth Barry with a cross.
41:50Attempt missed. James McArthur (Crystal Palace) left footed shot from the left side of the box misses to the left. Assisted by Jason Puncheon.
40:36Attempt missed. Yannick Bolasie (Crystal Palace) right footed shot from outside the box is too high. Assisted by Connor Wickham.
39:34Corner, Everton. Conceded by Yohan Cabaye.
38:33Corner, Everton. Conceded by Damien Delaney.
38:32Attempt blocked. Seamus Coleman (Everton) left footed shot from outside the box is blocked. Assisted by Gerard Deulofeu.
32:25Brendan Galloway (Everton) wins a free kick in the defensive half.
32:25Foul by Yohan Cabaye (Crystal Palace).
29:58Corner, Everton. Conceded by Scott Dann.
23:59Foul by Gareth Barry (Everton).
23:59Connor Wickham (Crystal Palace) wins a free kick on the left wing.
22:06Attempt missed. Arouna Koné (Everton) left footed shot from the left side of the box misses to the left. Assisted by Romelu Lukaku.
21:12Offside, Crystal Palace. James McArthur tries a through ball, but Yannick Bolasie is caught offside.
20:22Romelu Lukaku (Everton) hits the left post with a left footed shot from outside the box.
17:43Attempt blocked. Gareth Barry (Everton) right footed shot from outside the box is blocked.
16:57John Stones (Everton) wins a free kick in the defensive half.
16:57Foul by Jason Puncheon (Crystal Palace).
15:12Attempt missed. Mile Jedinak (Crystal Palace) right footed shot from outside the box is high and wide to the right. Assisted by Yohan Cabaye following a corner.
15:06Attempt saved. Connor Wickham (Crystal Palace) header from the left side of the six yard box is saved in the bottom left corner. Assisted by Yannick Bolasie with a cross.
14:56Attempt missed. Scott Dann (Crystal Palace) header from the right side of the six yard box misses to the left. Assisted by Jason Puncheon with a cross following a corner.
14:18Corner, Crystal Palace. Conceded by Ramiro Funes Mori.
12:00Corner, Crystal Palace. Conceded by Gerard Deulofeu.
6:23Attempt missed. Ross Barkley (Everton) right footed shot from the left side of the box is close, but misses to the right. Assisted by Romelu Lukaku.
5:11Attempt missed. Seamus Coleman (Everton) right footed shot from the right side of the box misses to the left. Assisted by Tom Cleverley.
3:29Seamus Coleman (Everton) wins a free kick in the defensive half.
3:29Foul by Jason Puncheon (Crystal Palace).
0:43Attempt saved. Connor Wickham (Crystal Palace) right footed shot from outside the box is saved in the bottom left corner. Assisted by James McArthur.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
Live data and text provided by our data suppliers