Kane and Son Heung-Min struck in the second half to earn Spurs their first Premier League win since Jan. 17.
The Spurs captain had missed the previous two defeats against Brighton and Chelsea but made a surprise start against Sam Allarydce's side.
"We've had a couple of bad results so it was very important to get back to winning ways," Son said.
"Harry is one of the best strikers in the world so we missed him, even if it was only a couple of games, and I'm happy that he scored again. I miss him."
The win sees Spurs leapfrog Chelsea into seventh place while West Brom remain 19th in the table.
The hosts dominated possession from the start and Kane almost opened the scoring after 15 minutes but his strike hit the bar.
Spurs finally broke the deadlock after 54 minutes when Pierre-Emile Hojbjerg found Kane inside the box to finish.
Kane becomes the joint-second highest scorer alongside Bobby Smith in the club's history with 208 goals behind Jimmy Greaves.
Son doubled Spurs' lead after he was on the end of a swift counter attack started from Lucas Moura.
West Brom posed a threat late on and Diagne then had two goals ruled out for offside. Spurs held on for the clean sheet and crucial three points.
"Kane is a special player, but today they showed everyone how together they are and how much they were suffering with the bad results," Spurs boss Jose Mourinho said postmatch.