Harry Kane made a welcome return for the LillyWhites, who dropped Eric Dier, Moussa Sissoko and Steven Bergwijn from Thursday's loss to Chelsea.
Kane could've capped his comeback with a goal from a loose pass into the area before the half-hour mark, but the forward dragged wide of the bottom-corner.
West Brom endured no breathing space with the end of the half in sight, as a diving header from Serge Aurier following a corner-kick produced a flying save of goalkeeper Sam Johnstone.
The Baggies at the other end got their first opening deep in the half through the head of Mbaye Diagne, but goalkeeper Hugo Lloris smothered.
Johnstone was at full stretch seconds in the second half with a stomping save from a thumping strike by Heung-Min Son following good work from Kane.
The Baggies finally succumbed to the pressure on 53 minutes after Kane got on the far side of the area to side-foot past Johnstone following a low pass from Pierre-Emile Hojbjerg.
It was two in the space of four minutes when a surging run towards the area by Lucas Moura allowed Son to gather possession to rifle in the top-corner.
West Brom thought they had pulled a lifeline through a smart finish from Diagne a minute later, but the strike was ruled out for offside.
An enforced substitution on the side of Spurs followed in the closing stages, as Aurier made way for Matt Doherty.
West Brom continued attempting a fight-back late on through Diagne amongst others, but the host held out to claim victory in the end.