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 and German champions Bayern Munich 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.
“I think we deserved more. It was a very tight first half. said Swansea manager Michael Laudrup
“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.”
Written by Steve Milne – Have your say below 🙂