West Brom had an early lead at the Hawthorns through Youssouf Mulumbu’s header but Tottenham leveled through Adebayor after his initial penalty kick had been parried by Ben Foster.
Jermain Defoe, who earnt a recall in place of injured Rafael van der Vaart, struck his seventh goal of the season with nine minutes remaining. Defoe beat Foster with a low drive from a flick by Adebayor after the Baggies defence back-tracked.
Defoe then had another close-range attempt deflected wide before Adebayor, on target twice against Aston Villa on Monday, grabbed his second goal off a pass from Gareth Bale in injury time.
Tottenham has now picked up 28 points from a 10-game unbeaten league run.
Spurs always threatened when they pushed forward as Albion ran out of steam and were unable to maintain the high tempo performance which served them well in the opening half.
Adebayor was a constant menace while midfielder Scott Parker was more of an influence in the final 45 minutes.
Foster looked unconvincing when fumbling a low 30-yard drive from Sandro around the post. But after 10 minutes Mulumbu put Albion ahead with his first goal of the season.
Zoltan Gera turned the ball back to Steven Reid whose cross was met by the unmarked Mulumbu who glanced a header past Brad Friedel into the corner of the net.
After 26 minutes Adebayor put Tottenham level with his sixth goal of the season.
Referee Lee Probert awarded a penalty after Aaron Lennon was pulled back by Nicky Shorey, the third penalty West Brom has conceded in its last three home games.
Adebayor’s spot-kick was blocked by Foster but the on-loan Manchester City striker converted the rebound and then put the result out of doubt in injury time.