Spurs were far from their best in West Midlands but Kane’s late intervention makes it four straight Premier League away wins for Jose Mourinho.
The Portuguese boss opted to hand Gareth Bale his first league start of the season against the Baggies but the Welsh international struggled to make an impact against the hosts.
Spurs did carve out a string of half chances in the opening 45, but the best chances fell to West Brom, as Callum Robinson tested Hugo Lloris.
West Brom worked hard to shut Tottenham out after the break with Sergio Reguilon’s long range drive well saved by Sam Johnstone.
With Tottenham unable find a breakthrough, they left the door open for the hosts on the counter attack, and Lloris produced another vital stop to deny Karlan Grant.
But with Mourinho driving them on from the touchline, Spurs began to turn the screw in the final 10 minutes.
Johnstone was at his best to deny Toby Alderweireld and Carlos Vinicius but he could do nothing as Kane’s finally broke their resistance.
Irish international Matt Doherty hung a cross into the box and with Johnstone was caught in no man’s land, as Kane stole in to nod home his 150th Premier League goal.
Full Time at The Hawthorns it’s West Brom 0 Tottenham 1