* Attacking Spurs fight back to win 3-2 at Southampton
* Everton leapfrog Chelsea as Barkley magic downs Swansea (adds Barkley quotes)
By Mark Meadows
LONDON, Dec 22 (Reuters) - Tim Sherwood's hopes of becoming Tottenham Hotspur's permanent manager were boosted after his attacking team came back to win 3-2 at stuttering Southampton in an enthralling Premier League game on Sunday.
Forgotten man Emmanuel Adebayor scored twice as caretaker boss Sherwood played the Togo striker up front with Roberto Soldado for the first time in a ploy which helped Spurs move above Manchester United into seventh spot.
Everton surged up to fourth, pending Chelsea's trip to Arsenal on Monday (2000 GMT), after England prospect Ross Barkley's perfect free kick six minutes from time secured a deserved 2-1 win at Swansea City.
Sherwood, who took over for two games at least when Andre Villas-Boas was sacked by Spurs after last weekend's 5-0 home thumping by Liverpool, threw caution to the wind in his bid to get the job full-time by also playing without a defensive midfielder.
It looked to have backfired when unmarked midfielder Adam Lallana grabbed the opener for Southampton on 13 minutes with a fine turn and shot from 20 metres.
Adebayor, who scored on his return to the team in the midweek League Cup loss to West Ham United, then expertly volleyed in Soldado's superb cross for a 25th-minute equaliser on his first league start of the season.
Spurs, who have now come from behind to win their last three away games, made a flying start to the second half and it was no surprise when Jos Hooiveld turned Danny Rose's low cross into his own goal on 54 minutes.
Southampton made it 2-2 when Rickie Lambert tapped in following more great work from England colleague Lallana but Adebayor sealed the win when he fired home after a ricochet on 64 minutes before Soldado missed three good chances.
"You enjoy it when you win. I did not enjoy the first half, I thought we were poor," Sherwood told Sky Sports.
"I need to speak to the chairman about how they want to take the club forward. That'll happen sooner rather than later I hope, as these guys need a manager.
"I like to set teams up like that (in an attacking manner). There are no rules, there are different ways to win a football match. You have to do what you believe."
As well as ex-Spurs manager Glenn Hoddle, who has said he wants the job again, Southampton boss Mauricio Pochettino has been touted in the media as a potential Tottenham target given his largely English side's youthful brand of pressing football.
However, they have now not won in six games and sit ninth, two spots above Swansea.
Everton in contrast are flying after a fourth victory in five games with midfielder Barkley particularly on fire.
The 20-year-old was again busy throughout in south Wales and sent his free kick crashing in off the bar as boss Roberto Martinez triumphed over his former club and saw his side go a point above Chelsea and only two off top.
"It was a relief as I had a chance to score with 20 minutes to go and I slipped," said Barkley, sporting a new shorn haircut.
"I told (Romelu) Lukaku to leave it as I'd seen the goal and thought, 'I'm going to score this'."
Everton opened the scoring after 66 minutes following sustained pressure when Seamus Coleman's fierce swerving shot was allowed in at the near post by keeper Gerhard Tremmel.
Swansea, suffering a hangover from last term's superb campaign and their Europa League exploits this season, were without injured talisman Michu and had brief hope when Dwight Tiendalli's 70th-minute prod deflected in off Bryan Oviedo.
Arsenal welcome Chelsea on Monday hoping to depose new leaders Liverpool, who beat Cardiff City 3-1 on Saturday. (Editing by Ed Osmond)