It looked as though West Brom had successfully stifled Tottenham’s formidable front trio of Kane, Gareth Bale and Son Heung-min, starting together in the league for the first time, but Kane headed home in the 88th minute.
Tottenham moved top, temporarily at least, with 17 points from eight matches while winless West Brom, who could count themselves unfortunate, remained third bottom f the standings.
Liverpool and Leicester City could both go above Tottenham if they win later on Sunday.
“I promise you I’m not bothered about Leicester versus Wolves or City versus Liverpool. I just want us to win games and then we’ll see where we are,” Spurs manager Jose Mourinho said.
“West Brom’s performance made us play in the way we did. They were very good defensively. We played safe.”