Dele Alli converted Toby Alderweireld's long pass to give us the lead after 15 minutes, but James McClean's header shortly before half-time saw the Baggies get back on level terms.
Hugo Lloris denied Jonas Olsson from point-blank range in the second period as we extended our unbeaten Premier League run to 14 games.
Spurs (4-2-3-1): Lloris (c), Walker, Vertonghen, Alderweireld, Rose; Dier, Dembele, Alli (Njie 79), Eriksen, Lamela (Son 65); Kane. Substitutes (not used): Vorm, Trippier, Wimmer, Winks, Onomah.
West Brom (5-4-1): Myhill, Dawson, Olsson, Evans, McAuley, Brunt; Sessegnon (Gardner 44), Morrison, Fletcher, McClean; Rondon. Substitutes (not used): Lindegaard, Chester, Anichebe, Lambert, Berahino, McManaman.
Goals: West Brom – McClean 39; Spurs – Alli 15.
Yellow cards: West Brom – Morrison 57, Gardner 73, McClean 83; Spurs – Kane 75, Dembele 81.
Referee: Jonathan Moss.