Spurs made five changes from the win over Ludogorets, with goalkeeper Hugo Lloris, Sergio Reguilon, Pierre-Emile Hojbjerg and Son Heung-Min all being recalled while West Brom were without Branislav Ivanovic and Matheus Pereira after they tested positive for Covid-19.
Callum Robinson nearly broke the deadlock for the hosts in the 26th minute with a cross from the byline that looped towards goal but Eric Dier rose high to head it off the line.
The Baggies were building up momentum after that, putting Spurs under pressure but they could not get clear chances with their long balls in the area while Tottenham were unable to pose any danger on counter-attacks as the first stanza ended without goals.
The match was much more lively in the early exchanges of the second stanza and Son came close to breaking the deadlock for Spurs just after the hour-mark with a low strike from a tight angle that was saved by goalkeeper Sam Johnstone.
Conor Gallagher was unlucky not to give Slaven Bilic's charges the lead in the 68th minute after beating two defenders to carve out space outside the box but his strike came off the post.
Karlan Grant thought he had finally given West Brom the lead three minutes later after glancing a good header at the near post from a corner but Loris produced a breathtaking save.
However, Harry Kane snatched the winner for Jose Mourinho's men in the last two minutes with a flicked header inside the six-yard box off Matt Doherty's cross.