The victory for fourth-placed Spurs, which came despite their only available forward Jermain Defoe limping off in the first half, put them a point behind Chelsea in third after Rafael Benitez's side lost 3-2 at Newcastle United on Saturday.
The Londoners were helped by West Brom's Macedonia defender Goran Popov being sent off after 48 minutes for spitting at Kyle Walker but Spurs deserved the win because of Welshman Bale's continued heroics.
The 23-year-old's 13th goal in all competitions this term, following another cracker in the 1-1 draw with Norwich City in midweek, summed up all his attributes as he evaded a challenge on the edge of the box and let fly with a swerving strike.
With Emmanuel Adebayor away at the African Nations Cup, Spurs' over reliance on out-of-form Defoe was keenly felt by supporters but Bale is digging them out of holes as a Champions League spot looks more and more a possibility.
Ninth-placed West Brom had decent chances through Shane Long and Romelu Lukaku but perhaps missed fellow forward Peter Odemwingie, dropped after turning up at Queens Park Rangers without permission on transfer deadline day as he tried to force through a move.
Second-placed Manchester City host Liverpool, in seventh, later (1600 GMT) hoping to close the 10-point gap on leaders Manchester United, who won 1-0 at Fulham on Saturday.
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- Jermain Defoe
- West Brom