Tottenham led twice through goals at the start of each half from Nacer Chadli and Christian Eriksen, but were pegged back by Adam Johnson’s solo effort and substitute Kane’s late own goal.
Spurs will be left to rue dropping two points after dominating most of the game and twice striking the woodwork as Sunderland earned their third draw of the season.
The visitors came flying out of the blocks and went close to scoring in the first minute as Eriksen slipped in Danny Rose inside the box and he fired in a shot which was pushed away by Vito Mannone.
Mauricio Pochettino’s side did not have to wait long to break the deadlock as a minute later Emmanuel Adebayor fired in a shot from the edge of the box which was parried out by Mannone and Chadli reacted quickest to fire home the loose ball.
The lead proved short-lived as within two minutes Sunderland drew level with their first attack of the game through Johnson.
The winger cut in from the left past a couple of Spurs challenges and fired in a shot which went through a couple of Spurs bodies to evade Hugo Lloris in the Tottenham goal and Rose on the line.
Tottenham almost restored their lead straight away as Chadli cut in from the left and curled in a shot which was well saved by Mannone.
The visitors looked dangerous every time they went forward in the opening exchanges and Adebayor should have scored on seven minutes when he latched onto Eriksen’s clever lofted pass only to see his point-blank volley kept out by the body of Mannone.
Tottenham dominated the first half and were inches away from regaining the lead on 38 minutes when Mousa Dembele let fly from fully 30 yards and was unlucky to see his shot come back off the post with Mannone stranded in the Sunderland goal.
Tottenham picked up where they left off at the start of the second half and grabbed the lead for the second time on 48 minutes when Patrick van Aanholt’s clearance from Chadli’s cross bounced off Wes Brown and fell to Eriksen inside the six-yard box and he stabbed the ball home from close range.
Erik Lamela was inches away from adding to Tottenham’s lead on 74 minutes with his first Premier League goal when his curling shot from the edge of the box came back off the crossbar.
Sunderland were gifted a way back into the game eight minutes from time as substitute Jordi Gomez fired over a free-kick from the left and Vlad Chiriches’ clearance cannoned off Kane and into the net.
The home side almost won it a minute from time when van Aanholt burst down the left and cut the ball back for Will Buckley on the penalty spot, but the winger lifted his shot over the crossbar.