Deli Alli came off the bench after an hour at White Hart Lane and it was his dummy that led to Ben Davies heading home the opener before Son Heung-min added a second.
Alli started on the bench as one of nine changes made by Mauricio Pochettino from the team that ended Chelsea's 13-match winning run on Wednesday.
Kane was left out of the squad completely after the striker spent the previous night attending to his partner Kate, who delivered their baby daughter, Ivy Jane, on Sunday morning.
Pochettino admitted he had planned to name Kane as a substitute but decided the striker should catch up on sleep instead.
"It is better now after a 2-0 win to explain," Pochettino said. "I want to send from here a big, big heart to Kate, his wife.
"It was a difficult night for her but now it's OK and they have a beautiful girl. Harry was more tired than his wife and we sent him to sleep.
"He spent all night at the hospital waiting and at 7.30am the baby was born. The plan was for him to be on the bench."