Son Heung-min netted the winner as Tottenham claimed a 1-0 win away to Burnley on Monday night.
Kane headed Erik Lamela’s pass into the path of Son, who headed home Spurs’ first effort on target on a night of few goal mouth action.
The effort means Son is now the division’s leading scorer with eight goals.
Burnley were unfortunate to lose with Ashley Barnes having a goal ruled out for offside and Kane clearing a James Tarkowski header off the line.
Ashley Westwood and Johann Gudmundsson also forced Hugo Lloris into saves.
Sean Dyche’s men remain in the relegation zone on one point, while Spurs move up from 11th to fifth.