The Spurs captain had missed the previous two defeats against Brighton and Chelsea but made a surprise start against Sam Allarydce's side.
Kane also saw a shot go just past the post before West Brom goalkeeper Sam Johnstone denied Serge Aurier with a brilliant save.
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.
"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.
- Harry Kane scores on return to help Spurs beat West Brom 2-0Washington Times
- Kane and Son double act gets Tottenham back on trackRTE.ie
- Harry Kane returns to spark Tottenham victory against West BromThe Guardian
- Harry Kane's return lifts Jose Mourinho as Tottenham end losing streakIndependent Online
- Harry Kane shakes Tottenham from attacking slumber as Jose Mourinho front-four offers blueprint for recoveryEvening Standard
- SportBBC News
- Harry Kane comeback inspires Tottenham to comfortable victory over West BromMirror.co.uk
- Three things we learned from Tottenham – West BromNBC Sports
- Kane returns to help Tottenham back to winning waysThe Peninsula Qatar
