Match ends, Swansea City 1, Everton 2.
Swansea City 1-2 Everton
Ross Barkley's stunning late free-kick helped Everton beat Swansea and move into the Premier League top four.
The 20-year-old midfielder missed a chance early in the second half and hit the bar from 20 yards before whipping the winner in off the crossbar.
In a frenetic second period, Seamus Coleman gave Everton the lead from 25 yards, before Dwight Tiendalli's volley was deflected in off Bryan Oviedo.
Everton, now 10 games unbeaten, sit two points off leaders Liverpool.
Toffees manager Roberto Martinez, who played for Swansea before guiding them to League One promotion as manager in 2008, said returning to south Wales brought back "great emotions" ahead of kick-off.
Barkley's winner will have sent the Spaniard back to Merseyside in similarly upbeat mood.
Everton, whose defenders have now contributed eight of their 29 league goals this season, have still only lost once in the league.
Only Italian side Roma, German champions Bayern Munich and Scottish Premiership leaders Celtic have lost fewer league games across Europe than the Toffees, whose verve and confidence was on show for all to see in the second half against Michael Laudrup's side.
As for Swansea, who have never beaten Everton, Sunday's defeat means they have recorded just two wins in nine outings.
Barkley, who made his England debut this year, wasted the game's best opening early in the second period when he lost his footing when through on Swansea goalkeeper Gerhard Tremmel.
But any Everton fears that the young Liverpudlian's confidence may be dented were squashed when he dribbled 30 yards to fire against the crossbar, before right-back Coleman netted his fourth of the season.
The Irishman's shot had too much pace and swerve for Tremmel, who was deputising for the injured Michel Vorm.
It was Swansea right-back Tiendalli who helped restore parity. His tame shot following a cross from the impressive Ben Davies deflected off Oviedo and wrong-footed goalkeeper Tim Howard.
The open and attacking nature of the second half made the first period largely forgettable.
Everton's Kevin Mirallas went closest to scoring before the break, forcing Tremmel into a near-post save but infuriating team-mates when he chose to shoot rather than passing to fellow Belgian Romelu Lukaku.
Laudrup, who distanced himself from links with the vacant Tottenham manager's post in midweek, watched as his side offered only wayward efforts from topscorer Wilfried Bony and Pablo Hernandez as the opening half drew to a close.
Goals from Coleman and Tiendalli ensured the fast start to the second half never dipped, before Barkley curled a majestic free-kick home from 25 yards to cap an eye-catching display.
The home side, now with just 10 points from 27 at home, rallied and Hernandez forced a good stop from Howard with a stinging shot.
Substitute Roland Lamah then had a volley expertly saved by the American goalkeeper in injury time.
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Swansea manager Michael Laudrup:
"I think we deserved more. It was a very tight first half.
"I liked our attitude in the whole game. There were not many chances in the first half, then second half they scored.
"We came back and I really thought Everton had settled for a draw with the changes they made.
"We tried until the end. Even after 1-1, we dominated."
Everton manager Roberto Martinez:
"We are really enjoying seeing Ross Barkley developing.
"It is a more significant three points than any you get in a glamorous fixture. We had a real focus and desire to win the game when we were not at our best. It tells a lot about the squad.
"For me, it is one of the most gratifying results."
- 33DaviesBooked at 83mins
- 20De GuzmánSubstituted forPozueloat 86'minutes
- 10BonySubstituted forAlvaroat 76'minutes
- 15RoutledgeSubstituted forLamahat 66'minutes
- 11MirallasSubstituted forOsmanat 78'minutes
- 17R Lukaku
- 22PienaarSubstituted forNaismithat 78'minutes
- Lee Mason
- Shots on Target
Second Half ends, Swansea City 1, Everton 2.
Ashley Williams (Swansea City) wins a free kick in the defensive half.
Foul by Leon Osman (Everton).
Foul by Dwight Tiendalli (Swansea City).
Ross Barkley (Everton) wins a free kick on the left wing.
Corner, Swansea City. Conceded by Tim Howard.
Attempt saved. Roland Lamah (Swansea City) right footed shot from outside the box is saved in the top right corner.
Pablo Hernández (Swansea City) wins a free kick on the right wing.
Foul by Ross Barkley (Everton).
Corner, Everton. Conceded by Ben Davies.
Foul by Jonjo Shelvey (Swansea City).
Ross Barkley (Everton) wins a free kick in the defensive half.
Offside, Swansea City. Pablo Hernández tries a through ball, but Álvaro is caught offside.
Attempt saved. Pablo Hernández (Swansea City) right footed shot from the right side of the box is saved in the top centre of the goal.
Substitution, Swansea City. Álex Pozuelo replaces Jonathan De Guzmán.
Corner, Swansea City. Conceded by Bryan Oviedo.
Goal! Swansea City 1, Everton 2. Ross Barkley (Everton) from a free kick with a right footed shot to the top right corner.
Ben Davies (Swansea City) is shown the yellow card for a bad foul.
Foul by Ben Davies (Swansea City).
James McCarthy (Everton) wins a free kick in the attacking half.
Attempt saved. Álvaro (Swansea City) right footed shot from the right side of the box is saved in the top left corner. Assisted by Jonjo Shelvey.
Delay over. They are ready to continue.
Substitution, Everton. Steven Naismith replaces Steven Pienaar because of an injury.
Substitution, Everton. Leon Osman replaces Kevin Mirallas.
Delay in match Steven Pienaar (Everton) because of an injury.
Offside, Everton. Tim Howard tries a through ball, but Ross Barkley is caught offside.
Substitution, Swansea City. Álvaro replaces Wilfried Bony.
Attempt missed. Jonjo Shelvey (Swansea City) right footed shot from outside the box is high and wide to the right. Assisted by Roland Lamah.
Attempt missed. Phil Jagielka (Everton) right footed shot from more than 35 yards is high and wide to the right.
Jonathan De Guzmán (Swansea City) wins a free kick in the defensive half.
Foul by James McCarthy (Everton).
Own Goal by Bryan Oviedo, Everton. Swansea City 1, Everton 1.
Attempt missed. Dwight Tiendalli (Swansea City) right footed shot from the centre of the box is close, but misses to the right. Assisted by Ben Davies with a cross.
Attempt blocked. Roland Lamah (Swansea City) right footed shot from outside the box is blocked. Assisted by Ben Davies.
Attempt saved. Gareth Barry (Everton) left footed shot from outside the box is saved in the bottom right corner. Assisted by Seamus Coleman.
Substitution, Swansea City. Roland Lamah replaces Wayne Routledge.
Goal! Swansea City 0, Everton 1. Seamus Coleman (Everton) right footed shot from outside the box to the top right corner. Assisted by James McCarthy.
Corner, Everton. Conceded by Gerhard Tremmel.
Attempt saved. Ross Barkley (Everton) left footed shot from outside the box is saved in the top right corner. Assisted by Gareth Barry.