Rafael van der Vaart put Harry Redknapp's side in front with an accomplished first-time finish after 19 minutes as Spurs, inspired by the brilliant Gareth Bale, dominated in front of their home supporters.
Though Swansea responded in the second half through a fine finish from Gylfi Sigurdsson - his sixth in 11 games following a January move from Hoffenheim - Tottenham secured a well-deserved victory thanks to two headers from Adebayor.
For Swansea it was a missed opportunity to go level with Liverpool in eighth, but Spurs were able to reflect on the rejuvenation of their Champions League challenge as they opened up a five-point gap over Chelsea and Newcastle United.
Having flitted between formations in recent months, Spurs were set up in the 4-2-3-1 shape that has served them so well for the majority of the season, with the sparky Luka Modric relishing the chance to dictate proceedings from the centre and Bale rampant down the left at a sunny White Hart Lane.
It was Modric who created the first chance of the afternoon after eight minutes as he drifted out to the left of the Swansea box and cut the ball back for Adebayor. He in turn found Van der Vaart arriving to the right and the Dutchman caressed his shot wide of the far post.
Sharp as he was at one end, Van der Vaart was also sloppy at the other and was lucky not to be punished for two mistakes as Wayne Routledge eventually drove a low shot wide against his former side.
However, Spurs remained firmly on top as their high-tempo approach served to unsettle a Swansea side used to dominating possession in the centre of midfield. Modric was enjoying time and space, while Bale tormented Swansea, accelerating past Leon Britton on one occasion before squaring for Adebayor, who failed to get the necessary contact at the near post.
When Tottenham did take the lead after 19 minutes, it was thanks to a lovely combination between their two star midfielders. Modric played a sumptuous ball down the line for Bale, and his cross was turned into the path of Van der Vaart by a desperate interception from Ashley Williams. The Dutchman pounced ruthlessly with an emphatic first-time finish from 20 yards.
Swansea were painting some pretty patterns with their passing game but without tangible reward. When Williams did get in behind Kyle Walker to meet a corner from Sigurdsson on the edge of the six-yard box, his header thumped into the turf and over.
Spurs had the greater cutting edge and Michel Vorm had to be alert to prevent them extending their lead before half time when Younes Kaboul forced him into a save when meeting a corner from Van der Vaart with a firm header.
Having produced little of note in the first half, Swansea were suddenly inspired by Sigurdsson as they started with far more intent in the second. Just five minutes after the restart the loan signing from Hoffenheim found a pocket of space 25 yards from goal and unleashed a fearsome effort that was headed for the top corner until Friedel scrambled across to tip it onto the post.
He would not be denied a second time though. Joe Allen saw a shot deflected up into the air and when it dropped for Routledge in the box he did superbly well to hold off his marker and chest the ball into Sigurdsson's path. The midfielder connected with a first-time effort that thumped into the turf and bounced into the far corner for 1-1.
However, Tottenham responded and found Bale to be a constant source of danger. The Wales international broke free once again on the left wing before finding Van der Vaart with a cute cross, only for the Dutchman's lovely angled header to be repelled by Vorm at his near post.
When Tottenham did edge in front again after 73 minutes it was Van der Vaart who claimed the assist, his corner finding Adebayor unmarked as the striker was allowed to jump unmolested and head home from five yards.
Adebayor repeated the trick on 86 minutes when rising again to meet a cross from the returning Aaron Lennon, on as a substitute to make his first appearance since March 7.
Bale was denied the goal his performance so richly deserved when seeing Vorm fling out an arm to block his firm drive in the final minutes, but Spurs still enjoyed a win which takes them back level with Arsenal.