Rafael van der Vaart gave the hosts the lead early in the first half but Swansea recovered after the break when Gylfi Sigurdsson found the net with a powerful shot into the ground.
With a point not enough for the hosts, they poured forward and were rewarded when their Togolese talisman nodded in a Van der Vaart corner and then a chipped cross from Aaron Lennon.
The win sees Spurs remain fourth but stay five points clear of Chelsea and move level with Arsenal after the Gunners slipped up against QPR yesterday.
It was a much needed win for Spurs but Swansea boss Brendan Rogers, who had earlier been linked with a managerial move to White Hart Lane, felt his side deserved more after putting on a strong display at one of the league’s top sides.
“We’re obviously disappointed with the score line but to come here and compete with a team challenging for the title is fantastic,” he said.
“Obviously I’m very proud of the players. In the first 20 minutes we had control of the game but they probably had more of the half after that. In the second half we were superb and some of our play and movement was fantastic.
“I can only give credit to the players and to our supporters who were brilliant for us today. Our players put on a real performance and it’s just a shame about the result.”
Swansea impressed throughout with their stylish passing, but it was the home side who pressed high and took an early lead.
Luka Modric’s sublime pass set Gareth Bale free down the left and, despite blocking the cross, Ashley Williams deflected the ball straight into the path of van der Vaart who stroked it home.
Swansea were energised after the interval and, once Brad Friedel had kept out Sigurdsson’s 25-yard drive with a stunning save, the Icelander levelled the score with a shot that bounced over the Tottenham stopper.
Spurs reacted to the equaliser by attacking in greater numbers and the hosts restored their lead when Adebayor nodded in a simple header from a Van der Vaart corner.
The on-loan striker then sealed the points with another headed effort after Lennon, returning from a hamstring injury, chipped his cross to the back post for Adebayor to nod in.
The win was the hosts’ first in the league since beating Newcastle 5-0 back in February and, with no games left to play against sides in the top eight, Tottenham have given their Champions League hopes a significant boost.
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