"I told Romelu Lukaku to leave it, because I saw the goal and thought, 'I'm going to score this'," said Barkley. "I don't really practise free-kicks because Leighton Baines is usually on the pitch, but I thought it was my chance."
Manager Roberto Martinez said: "Ross is growing game by game. The goal, technically, is as good as it gets. A lot has been said about Ross, but it's always an understatement. He's an incredible listener and a young man with a lot of potential. He always comes up with something different in a game to show he can develop. We didn't know he could take free-kicks, but it's good to know from now on."
Seamus Coleman had given Everton a 66th-minute lead with a ferocious strike, but they were pegged back when Bryan Oviedo put Dwight Tiendalli's off-target effort into his own net.
But Everton were not to be denied and up stepped Barkley with six minutes to go to beat Gerhard Tremmel with a free-kick which nicked the underside of the crossbar on its way in. The Merseysiders thoroughly merited their success, which tees up back-to-back home games against Sunderland and Southampton.
Swansea manager Michael Laudrup also had praise for Barkley. "He is a great talent, he is a great runner with the ball, he can play in tight areas, he is definitely a big talent."
Laudrup confirmed Swansea are set to make a decision on whether Michu undergoes surgery on an ankle injury. "We will know more tomorrow," he said. "If tomorrow the information suggests he needs an operation he will have surgery in the very near future."
Meanwhile, Tottenham Hotspur interim manager Tim Sherwood hopes to hold talks today with chairman Daniel Levy to find out whether he will be staying on as Andre Villas-Boas' successor.
Sherwood's first match at the helm resulted in a Capital One Cup exit to West Ham, but yesterday he oversaw his first victory with an attack-minded display at Southampton.
Emmanuel Adebayor netted either side of a Jos Hooiveld own goal as Spurs ran out 3-2 victors, resulting in bookmakers immediately shortening odds on the former midfielder being handed the reins on a permanent basis. The win will certainly not do those chances any harm and Sherwood hopes to take control of the Boxing Day clash with West Bromwich Albion with a clearer idea on his future.
If Sherwood ends up only being at the helm for a short period, whoever comes in will be thanking him for rejuvenating Adebayor. Having been cast aside by Villas-Boas, the Togo striker has scored three goals in two starts under the interim manager and was superb throughout at St Mary's. "Listen, we all know Adebayor, we all know he's a top player," Sherwood said. "He doesn't need any motivating."
The victory stops the rot at Spurs, but continues Southampton's frustrating recent form. Saints, who took the lead through Adam Lallana and made it 2-2 through Rickie Lambert, have now gone six matches without a win, hardly the best preparation for trips to Cardiff and Everton.