The Togolese striker settled an evenly balanced game with an adroitly taken strike in the 65th minute to take Tottenham above Everton and into fifth place in the battle for a top-four finish.
Tim Sherwood's side now trail fourth-place Liverpool by three points, with Everton two points back in sixth and Manchester United five points further back ahead of their home game with Fulham later on Saturday.
Everton were boosted by the return from injury of goalscoring right-back Seamus Coleman and they made an enterprising start to the game at White Hart Lane, with Leon Osman to the fore.
The diminutive English midfielder had four sights of goal in the first eight minutes, curling a left-foot shot wide from just outside the area and then extending Spurs goalkeeper Hugo Lloris with a crisp half-volley.
Osman headed wide from the subsequent corner and then drove straight at Lloris from a Steven Naismith pass, while Kevin Mirallas fired over after a weaving run.
Spurs' best chances of the first half saw Tim Howard save at Mousa Dembele's feet after Sylvain Distin undercooked a back-pass, before an inviting Danny Rose cross narrowly eluded the sliding Adebayor.
Andros Townsend made his return for Spurs in the second half after missing nine games with a hamstring problem and minutes later the hosts went ahead.
Kyle Walker caught the Everton defence on their heels with a quickly taken free-kick and Adebayor did the rest, chesting the ball down and resisting the attentions of Coleman before drilling a low shot past Howard.
It was Tottenham's first shot on target of the match, but it proved enough to secure victory despite Coleman having an injury-time penalty appeal turned down after tumbling over a challenge from Etienne Capoue.
Manchester United will look to close the 10-point gap separating them from Liverpool later on Sunday when they welcome bottom club Fulham to Old Trafford.
It will be United captain Nemanja Vidic's first appearance since he announced that he will leave the club at the end of the season.
Fulham, managed by former United assistant coach Rene Meulensteen, are currently five points adrift of safety and were knocked out of the FA Cup by third-tier Sheffield United in mid-week.
Source : AFP
Source: AFP