Albion were given an early lead through Youssouf Mulumbu’s header but levelled through Adebayor after his initial penalty had been parried by Ben Foster.
Jermain Defoe struck his seventh goal of the campaign with nine minutes remaining and then Adebayor, on target twice against Aston Villa on Monday, added a third in injury time.
It was no more than Tottenham deserved after dominating the second period and they have now picked up 28 points from a 10-game unbeaten league run in their push for a place in the Champions League.
They 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.
Albion keeper Ben 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 campaign.
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.
Albion suffered a setback after 20 minutes when Gera went down clasping his left knee unchallenged. He was unable to continue after treatment and was replaced by Simon Cox.
Sandro became the first player to be yellow carded a minute later for a challenge on James Morrison.
After 26 minutes Adebayor put Tottenham level with his sixth goal of the campaign.
Referee Lee Probert awarded a penalty after Aaron Lennon was pulled back by Nicky Shorey, the third Albion have conceded in their last three home games.
Adebayor’s spot-kick was blocked by Foster but the on-loan Manchester City striker converted the rebound.
Albion appealed in vain for a penalty after Kyle Walker challenged Thomas but it was an optimistic shout as there appeared little contact.
Foster held on to a curling attempt from Defoe while Albion defender Gareth McAuley was adjudged to have fouled Friedel as Albion claimed he had carried a Reid cross over his own goal-line.
Mulumbu was booked for dissent after making his feelings known to referee Probert when brought down by Sandro.
Friedel blocked a low shot from Mulumbu with his legs after he had made a purposeful run
Tottenham made a bright start to the second period and Parker teed up an early chance for Adebayor.
But Foster was equal to his rising shot which he parried out.
Cox should have done better when unmarked but he headed straight at Friedel from Morrison’s inviting centre.
Reid came to Albion’s rescue when he cleared Defoe’s goal-bound shot from a narrow angle after he had evaded Olsson and Foster.
Foster made another fine save to block a point-blank range effort from Adebayor after a deflected cross from Bale had broken to him.
Brunt was booked for hauling back Benoit Assou-Ekotto.
Roy Hodgson made his first change after 72 minutes with the limping Long replaced by Peter Odemwingie.
Reid made a crucial tackle to take the sting out of an Adebayor shot which trickled through to Foster.
At the other end Brunt fired over from 10 yards out after a pull-back by Thomas as Albion came more into the game.
With nine minutes left Defoe beat Foster with a low drive from an Adebayor flick after the Baggies defence back-tracked.
Defoe then had another close range attempt deflected wide and Adebayor shot past the post from close range.
Adebayor made it 3-1 in stoppage time from a Bale pass.