Gerard Deulofeu produced a dazzling display as Everton reached the League Cup semi-finals with a comfortable win over Middlesbrough.
The ex-Barcelona player stunned the Boro defence in the 20th minute when he weaved past two challenges before placing his low shot past Tomas Mejias.
Deulofeu then produced a series of stepovers before delivering a cross for Romelu Lukaku who headed in for 2-0.
Stewart Downing went closest for Boro with a strike that was tipped over.
Roberto Martinez's Everton side will face a Premier League side in the last four when the draw is made on Wednesday, after Southampton's match against Liverpool. Stoke and Manchester City are also in the draw following their wins on Tuesday.
The 21-year-old was seen as surplus to requirements at Barcelona when he was sent on loan to the Toffees in 2013 before joining on a permanent deal in the summer.
At the Riverside Stadium, the Spaniard provided two magical moments which would not have looked out of place at the Nou Camp.
His solo strike came just before midway in the first half. The Spaniard made a beeline for the goal, swept past two challenges, leaving defender Ben Gibson on the floor, before firing into Meijas' right-hand corner.
But perhaps the best goal of the game was the second, when he set up Lukaku for the Belgian's 13th in 18 games.
On this occasion, Deulofeu was out on the right. He made six stepovers in front of Boro defender Fernando Amorebieta, before shifting the ball to his right foot and finding the 6ft 3in striker with a great ball.
"Gerard is a young man in terms of the amount of games that he's played at this level, so he needs a lot of games," said Martinez. "But as a natural talent, he's as good as it gets.
"He's got that talent that you dream to have, he's got the talent that anyone would pay for a ticket to watch him."
Manager Aitor Karanka might concede that his side were undone by two brilliant goals, however the home side should have posed more problems for the visiting defence.
Only Downing tested Joel Robles in the Everton goal, and appeals for handball against Ramiro Funes Mori in the second half were half-hearted. Referee Roger East was not interested and replays suggested it would have been harsh to penalise the Argentine defender.
Despite going 2-0 down in 28 minutes, Boro did not capitulate and instead improved markedly after the break. Karanka's men can take heart from Tuesday's display as they return to Championship action and the fight for promotion.
There was a touching moment in the 33rd minute when fans inside the stadium switched on the torches on their phones and sang "Ali Brownlee is one of our own".
It was a tribute to the BSports Tees commentator Ali Brownlee, who has been diagnosed with bowel cancer. Brownlee has been commentating on Middlesbrough matches for 33 years.
John Murray, who was commentating for BSports Radio 5 live, said: "He's an absolutely top fella. A thoroughly nice guy. This tribute will mean a lot to him."
Middlesbrough boss Aitor Karanka:
"It reminds me of playing against Arsenal last season.
"They played with their best starting 11 and Everton did the same, I take that as a complement. They were better than us, really good players in a really good team with a really good coach.
"That said, one goal can change a game and I thought if we had scored on 85 or 90 minutes there could have been a big finish."
Everton manager Roberto Martinez:
"It was a fantastic occasion to be involved in the cup. We had to be mature and control the game and we did that really well, especially after the Bournemouth result. It showed we learnt a lot.
"It is a terrific feeling to get through to the semi-final and good memory for our football club.
"Middlesbrough had a team who are good on the ball but we defended really well. All in all, the two goals were exceptional pieces of quality. More than anything, after keeping a clean sheet from going 2-0 up was very pleasing."
Everton could move up into the top six in the Premier League if they defeat Crystal Palace next Monday, while Boro could take top spot in the Championship if they beat Ipswich at Portman Road on Saturday.
Full Time Match ends, Middlesbrough 0, Everton 2.
90:00 +4:08 Full timeFull Time Second Half ends, Middlesbrough 0, Everton 2.
90:00 +3:44Ross Barkley (Everton) wins a free kick in the attacking half.
90:00 +3:44Foul by Daniel Ayala (Middlesbrough).
90:00 +0:56Steven Naismith (Everton) wins a free kick on the left wing.
90:00 +0:56Foul by Daniel Ayala (Middlesbrough).
90:00 +0:05Delay over. They are ready to continue.
89:44Delay in match (Everton).
89:19Attempt saved. Grant Leadbitter (Middlesbrough) right footed shot from outside the box is saved in the bottom left corner.
88:30 BookingBooking John Stones (Everton) is shown the yellow card for a bad foul.
88:22Foul by John Stones (Everton).
88:22Stewart Downing (Middlesbrough) wins a free kick in the attacking half.
85:16 SubstitutionSubstitution Substitution, Everton. Steven Naismith replaces Romelu Lukaku.
84:34Foul by Ramiro Funes Mori (Everton).
84:34Cristhian Stuani (Middlesbrough) wins a free kick in the defensive half.
84:07Attempt saved. Kevin Mirallas (Everton) right footed shot from outside the box is saved in the bottom left corner. Assisted by Seamus Coleman.
83:27Gareth Barry (Everton) wins a free kick on the right wing.
83:27Foul by Cristhian Stuani (Middlesbrough).
82:05 SubstitutionSubstitution Substitution, Middlesbrough. George Friend replaces Ben Gibson.
80:36 SubstitutionSubstitution Substitution, Everton. Kevin Mirallas replaces Gerard Deulofeu.
Attempt missed. Ross Barkley (Everton) right footed shot from outside the box is high and wide to the left following a set piece situation.
78:53Leighton Baines (Everton) wins a free kick on the left wing.
78:53Foul by Albert Adomah (Middlesbrough).
78:20Seamus Coleman (Everton) wins a free kick in the attacking half.
78:20Foul by Grant Leadbitter (Middlesbrough).
77:38Delay over. They are ready to continue.
77:20Delay in match Gerard Deulofeu (Everton) because of an injury.
76:40 BookingBooking Leighton Baines (Everton) is shown the yellow card.
73:42Attempt blocked. Romelu Lukaku (Everton) left footed shot from the right side of the box is blocked. Assisted by Joel Robles.
73:19Attempt saved. Adam Forshaw (Middlesbrough) right footed shot from outside the box is saved in the bottom right corner. Assisted by Fernando Amorebieta.
72:59 SubstitutionSubstitution Substitution, Middlesbrough. Albert Adomah replaces Adam Clayton.
72:49 SubstitutionSubstitution Substitution, Everton. Leighton Baines replaces Brendan Galloway.
71:23Corner, Middlesbrough. Conceded by Brendan Galloway.
69:35Attempt missed. Cristhian Stuani (Middlesbrough) header from the centre of the box is just a bit too high. Assisted by Nsue with a cross.
62:25Corner, Everton. Conceded by Adam Clayton.
62:24Attempt blocked. Ross Barkley (Everton) right footed shot from outside the box is blocked. Assisted by Gerard Deulofeu.
58:10Corner, Middlesbrough. Conceded by Joel Robles.
58:04Attempt saved. Stewart Downing (Middlesbrough) left footed shot from outside the box is saved in the top centre of the goal.
55:22Attempt missed. Adam Clayton (Middlesbrough) right footed shot from outside the box is close, but misses to the left. Assisted by Adam Forshaw.
54:08John Stones (Everton) wins a free kick in the defensive half.
54:08Foul by Adam Forshaw (Middlesbrough).
49:13Gareth Barry (Everton) wins a free kick in the defensive half.
49:13Foul by Daniel Ayala (Middlesbrough).
48:43Corner, Middlesbrough. Conceded by John Stones.
48:40Attempt blocked. Grant Leadbitter (Middlesbrough) right footed shot from outside the box is blocked. Assisted by Adam Forshaw.
46:48 BookingBooking Fernando Amorebieta (Middlesbrough) is shown the yellow card for a bad foul.
46:38Gerard Deulofeu (Everton) wins a free kick in the defensive half.
46:38Foul by Fernando Amorebieta (Middlesbrough).
45:00Second Half begins Middlesbrough 0, Everton 2.
45:00 SubstitutionSubstitution Substitution, Middlesbrough. Adam Forshaw replaces Carlos De Pena.
45:00 +1:05 Half timeHalf Time First Half ends, Middlesbrough 0, Everton 2.
44:16Romelu Lukaku (Everton) wins a free kick in the attacking half.
44:16Foul by Fernando Amorebieta (Middlesbrough).
43:36Attempt missed. Stewart Downing (Middlesbrough) left footed shot from outside the box is close, but misses to the right from a direct free kick.
42:49Foul by Romelu Lukaku (Everton).
42:49Cristhian Stuani (Middlesbrough) wins a free kick in the attacking half.
41:40Leon Osman (Everton) wins a free kick on the right wing.
41:40Foul by Adam Clayton (Middlesbrough).
39:07Attempt missed. Kike (Middlesbrough) right footed shot from outside the box is high and wide to the right. Assisted by Ben Gibson.
38:09Attempt missed. Cristhian Stuani (Middlesbrough) right footed shot from outside the box misses to the left. Assisted by Stewart Downing.
36:26Attempt missed. Kike (Middlesbrough) right footed shot from outside the box is close, but misses to the left. Assisted by Cristhian Stuani.
35:55Attempt blocked. Ross Barkley (Everton) right footed shot from the left side of the box is blocked. Assisted by Romelu Lukaku.
34:36Attempt saved. Cristhian Stuani (Middlesbrough) right footed shot from the right side of the box is saved in the bottom left corner. Assisted by Adam Clayton.
30:48Leon Osman (Everton) wins a free kick in the attacking half.
30:48Foul by Grant Leadbitter (Middlesbrough).
29:27Offside, Middlesbrough. Stewart Downing tries a through ball, but Carlos De Pena is caught offside.
27:40 Goal scoredGoal! Goal! Middlesbrough 0, Everton 2. Romelu Lukaku (Everton) header from the right side of the six yard box to the top left corner. Assisted by Gerard Deulofeu with a cross.
23:52Offside, Middlesbrough. Fernando Amorebieta tries a through ball, but Kike is caught offside.
19:23 Goal scoredGoal! Goal! Middlesbrough 0, Everton 1. Gerard Deulofeu (Everton) right footed shot from outside the box to the bottom left corner. Assisted by Ramiro Funes Mori.
18:17Brendan Galloway (Everton) wins a free kick in the defensive half.
18:17Foul by Cristhian Stuani (Middlesbrough).
17:24Joel Robles (Everton) wins a free kick in the defensive half.
17:24Foul by Cristhian Stuani (Middlesbrough).
16:55Corner, Middlesbrough. Conceded by Joel Robles.
16:50Attempt saved. Stewart Downing (Middlesbrough) left footed shot from outside the box is saved in the top right corner.
15:59Foul by Ramiro Funes Mori (Everton).
15:59Cristhian Stuani (Middlesbrough) wins a free kick in the attacking half.
13:28Corner, Middlesbrough. Conceded by John Stones.
12:14Offside, Everton. Ross Barkley tries a through ball, but Seamus Coleman is caught offside.
12:00Ross Barkley (Everton) wins a free kick in the attacking half.
12:00Foul by Adam Clayton (Middlesbrough).
10:30Corner, Everton. Conceded by Fernando Amorebieta.
7:11Corner, Everton. Conceded by Fernando Amorebieta.
7:10Attempt blocked. Romelu Lukaku (Everton) header from very close range is blocked. Assisted by Gareth Barry with a headed pass.
6:38Corner, Everton. Conceded by Ben Gibson.
6:35Attempt blocked. Ross Barkley (Everton) left footed shot from outside the box is blocked.
2:36Foul by Adam Clayton (Middlesbrough).
2:36Leon Osman (Everton) wins a free kick in the defensive half.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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