Arsene Wenger’s edged into a first-half lead after Hector Bellerin teed up Aaron Ramsey to break the deadlock from close range.
However, Tottenham were handed a boost when Francis Coquelin was sent off for a second bookable offence early in the second half.
And Tottenham defender Toby Alderweireld levelled five minutes later before Kane edged Spurs into a 2-1 lead with 28 minutes remaining thanks to a brilliant strike.
But Mauricio Pochettino’s side couldn’t hold on for a valuable three points as Alexis Sanchez netted an equaliser for 10-man Arsenal with 16 minutes remaining.
Tottenham striker Kane promised Spurs fans that Pochettino’s men would be ready for their next league game at Aston Villa on Sunday 13 March.
— Harry Kane (@HKane) March 5, 2016
Kane has scored 17 times in 29 Premier League games so far this season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news