A close encounter swung in Spurs' favour three minutes into the second half when Baggies full-back Goran Popov was shown a straight red card for spitting at Kyle Walker.
Andre Villas-Boas' side were able to make their numerical advantage count on 67 minutes, with Bale shifting the ball onto his left foot and firing a 20-yard thunderbolt past a helpless Ben Foster.
The first half chance fell to Albion after Romelu Lukaku's flick-header found the recalled Shane Long in space and with only Hugo Lloris to beat. But his first touch was heavy and forced him out wide and he eventually overran the ball which went harmlessly out of play.
Lukaku was causing plenty of problems and the on-loan Chelsea striker forced a low save out of Lloris after good play by Baggies skipper Chris Brunt.
West Brom goalkeeper Ben Foster came quickly off his line to hack the ball away from Jermain Defoe after he had anticipated a through pass from Bale.
Lloris pulled off a fine save to prevent the home side going ahead after 20 minutes. Graham Dorrans threaded a pass through the Tottenham rearguard to Long who took the ball in his stride and raced into the box. But Lloris was equal to the situation and blocked the resulting shot from the Republic of Ireland international.
Defoe, in front of England head coach Roy Hodgson, needed touchline treatment after landing awkwardly on his left ankle when avoiding a challenge from Long. He was unable to continue and was helped down the tunnel by two Spurs physios and replaced by transfer window signing Lewis Holtby - leaving Andre Villas-Boas desperately short on striking options.
Lukaku shot over from a narrow angle and in first-half injury time Foster tipped a dipping effort from Bale over the bar.
Albion were reduced to 10 men after only three minutes of the second half. Replays showed that Popov spat in the direction of Spurs defender Kyle Walker after the two had squared up to each other. Referee Marc Clattenburg instantly brandished a red card at the on-loan Dynamo Kiev left-back.
It was one-way traffic towards the Albion goal from that point on and Foster turned aside a low drive from Holtby. The former England international was also alert in blocking a close-range attempt from Bale.
But after 67 minutes a stunning strike from Bale put Tottenham in front. The winger, playing in a more central role, received a pass from Walker, brushed off the challenge of Brunt and his 20 yard shot flew past the despairing dive of Foster into the top corner of the net.
Foster did well to block Clint Dempsey's shot as Spurs searched for a second goal, but one was enough to consolidate their top-four standing and take them to within a point of third-placed Chelsea.