Adebayor’s goals, separated by a Chico Flores own-goal, ensured Tottenham remained unbeaten in the league under manager Tim Sherwood, whose record now stands at five wins and a draw since the Englishman replaced sacked predecessor Andre Villas-Boas.
For Swansea, an eighth successive league match without a win left Michael Laudrup’s men just three points above the relegation zone.
The Welsh club had early chances at the Liberty Stadium, with Hugo Lloris saving Jonjo Shelvey’s long-range shot and striker Wilfried Bony hitting the crossbar when the France goalkeeper had been beaten by a powerful shot.
Swansea also had appeals for a penalty rejected by referee Martin Atkinson after Ivory Coast forward Bony was pushed in the back by Spurs defender Michael Dawson inside the box.
But, against the run of play, Togo international Adebayor gave Spurs a 35th minute lead when he powered in a header following an excellent first-time cross from Christian Eriksen.
And the north London side made it 2-0 in the 53rd minute when Flores turned Kyle Walker’s cross into his own net with Spurs’ Nacer Chadli waiting behind him.
Spurs wasted a chance to make it 3-0 when Mousa Dembele shot wide with Adebayor unmarked just yards from goal.
However, Adebayor’s fury turned to joy when, moments later, Spurs again opened up the frail Swansea defence.
Danny Rose did not repeat Dembele’s mistake but instead squared the ball to Adebayor who tapped from in from close range in the 71st minute.
Bony pulled a goal back seven minutes later with a shot from the edge of the box but it was all too late for Swansea.
“Even when they (Swansea) were having a lot of possession I thought we were the most dangerous side and it was just a matter of time before we clicked and found that final ball, and we did that many times in the second half and we could have gone on and won more comfortably,” Sherwood told Sky Sports.
Turning to Adebayor, the Spurs boss added: “It’s great. It’s obviously great for the football club and great for Ade himself, who’s flying at the moment and enjoying his football.
“He plays with a smile on his face and he’s finding the back of the net.”
Sunday’s other top-flight match sees high-flyers Chelsea at home to Manchester United.
The Blues will kick off nine points in front of faltering champions United, who will be without injured striker Wayne Rooney and Robin van Persie.
Victory for Jose Mourinho’s Chelsea would see them move to within a point of league leaders Arsenal.
By contrast, a United defeat at Stamford Bridge would increase the pressure on boss David Moyes, whose team are currently an unusually lowly seventh in their first season since the retirement of Alex Ferguson, Britain’s most successful manager.