Kane had not featured since going off at half-time during last month’s defeat to Liverpool at Anfield and was not expected to be fit after ankle problems until next week.
However, the forward was included in Jose Mourinho’s line-up and opened the scoring shortly after half-time before Heung-min Son added a second soon after.
After missing a couple of chances in the first half Kane struck in the 54th minute to move joint second on Tottenham’s all-time scoring list alongside Bobby Smith with 208 goals.
Four minutes later Son Heung-min drove in Tottenham’s second after a strong run by recalled Lucas Moura.
West Brom spent most of the time defending solidly but could have gone ahead on the stroke of halftime when Mbaye Diagne’s header was kept out by Hugo Lloris while Diagne also had two goals rightly ruled out for offside.
Tottenham moved up to seventh place with 36 points from 22 games, above Chelsea on goal difference before their match against bottom club Sheffield United later.
Sam Allardyce’s West Brom are 19th with 12 points from 23 games, 11 points below 17th-placed Burnley, and their hopes of avoiding relegation are looking forlorn.
Additional reporting by Reuters.