The 20-year-old bent a 25-yard effort beyond Gerhard Tremmel with six minutes remaining to ensure the Everton juggernaut barged its way back into the Premier League’s top four.
To make it all the more remarkable Barkley said after the game that he hadn’t been practicing free kicks, giving us a further glimpse of the immense natural talent he possesses.
Despite Michael Laudrup’s post-match claims to the contrary, the Toffees fully deserved all three points for a much-improved second half display in South Wales.
Still, for a while it looked like they would be forced to accept a point after Bryan Oviedo’s own goal cancelled out Seamus Coleman’s howitzer on 56 minutes.
With two home games over Christmas and the teams around us all playing each other, the importance of this win may only become apparent by the start of the new year, but there was a feeling at the final whistle that a significant hurdle had been cleared.
Only Bayern Munich and Roma have lost fewer games across Europe's major leagues; Everton are mixing it with the big boys and the fans are loving it.
The game’s explosive finish was a far cry from its tepid opening, the opening 45 a classic case of both teams cancelling each other out.
The only real chances of note both came from Kevin Mirallas, who saw one effort saved at the near post before seeing another blocked, with a furious Romelu Lukaku better placed for the pass.
A stern team talk later and the players appeared reinvigorated in the second half and gradually took control of the game.
They could – and perhaps – should – have taken the lead when Pienaar played in Barkley, but the midfielder slipped just as he was about to shoot and the chance went begging.
With Leighton Baines still absent, Coleman appears to have taken on the mantle of rampaging fullback and his growing influence on the game coincided with Everton’s best spell.
The Irishman first showed immense speed to reach the ball at the by-line and fire a low cross that Chico stretched to clear.
He then went on another barnstorming run right to the heart of the Swans’ defence before being denied by a last-gasp tackle from Ashley Williams.
Barkley, complete with new skinhead haircut, was also starting to impress and one of his trademark surging runs resulted in a left-footed drive that Tremmel did well to tip over.
Just when you thought it wasn’t to going to be Everton’s day, Coleman finally broke the deadlock in spectacular style on 68 minutes.
The 25-year-old marauded forward down the right once more and, after collecting McCarthy’s pass, unleashed a fizzing right-footed shot that swerved away from Tremmel and into the top corner.
That should have been the catalyst for the visitors to finish the game off, so it was hugely frustrating when the Swans drew level four minutes later.
Ben Davies’ cross from the left reached Dwight Tiendalli, whose shot looked to be going wide before it deflected off Oviedo and bobbled past a wrong-footed Howard.
The home side looked set for a point they barely deserved after being on the back foot for much of the second half.
However, this season Everton have developed a veneer of brilliance that helps them rise above the rest, with another piece of magic proving the difference here.
After McCarthy had been crudely body checked 25 yards from goal, Barkley curled the ball around the wall, beyond the reach of Tremmel and in off the crossbar to send the travelling Evertonians ballistic.
Swansea galvanised themselves for one final surge at the Everton goal, but Tim Howard was alert to push away Pablo Hernandez’s effort at the near post before tipping over Roland Lamah’s long-range volley.
The win sends Everton above Chelsea (for 24 hours at least) and with two home games to over Christmas; the opportunity is there for Everton to top the table going into 2014.
They once again failed to reach the heights at the Liberty Stadium that they have done this season, but, like the Fulham game, they ground out a crucial win.
And with a diamond like Barkley in the heart of the midfield, you really get the feeling that anything is possible.
Howard 8 Coleman 9 Jagielka 7 Distin 7 Oviedo 7 Pienaar 6 (Osman 6) McCarthy 7 Barry 8 Barkley 9 Mirallas 6 (Naismith 6) Lukaku 7
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