It seemed the visitors would get back to winning ways when Christian Eriksen put them ahead just after half-time, with Adam Johnson having earlier cancelled out Nacer Chadli's strike at the Stadium of Light.
But after Erik Lamela rattled the woodwork, Sunderland earned a share of the spoils when Will Buckley's free-kick hit Kane and flew into the net.
Both sides entered the game having fallen to disappointing defeats prior to the international break.
Tottenham lost 3-0 to Liverpool, while Charlie Austin grabbed the only goal as Sunderland were defeated by QPR.
And neither was able to get a desired three points this time around, although Gus Poyet will surely have been the happier of the managers.
There was little hangover from the two-week absence as Tottenham flew out of the blocks, Danny Rose forcing a fine save from Vito Mannone after the visitors cut through their opponents with ease.
Any disappointment at that miss was soon extinguished, Chadli continuing his fine start to the season by slotting home following a Mannone parry that kept out Emmanuel Adebayor's powerful strike.
Yet Sunderland regrouped and responded immediately when a fine counter-attack ended with Johnson's deflected effort beating Hugo Lloris.
The breathless start continued, though, with Mannone having to be on high alert to deny Chadli and Adebayor in quick succession.
Things unsurprisingly calmed down, although Tottenham still looked a constant threat as Eriksen - who had assisted Adebayor's chance with a sumptuous lob - cleverly found pockets of space.
It was Mousa Dembele who was next to threaten, taking advantage of being afforded too much space when unleashing a vicious left-footed strike from long range that rattled the post.
The second period begin in the same manner as the first, Eriksen putting Tottenham back in front.
Chadli was again instrumental, sending in a cross that Patrick van Aanholt could only clear into Wes Brown, the ricochet leaving Eriksen with the simplest of finishes.
Much like after the opening goal, Sunderland were suddenly spurred into life - although an end product to their endeavour was severely lacking.
Johnson was still looking dangerous for Poyet's men, however, as he showed when firing a powerful 25-yard effort inches wide.
That was one of the rare moments of excitement for the home support, with Tottenham still looking in control amid their back four showing great composure.
Yet they could still not find the goal that would provide more comfort for the visiting faithful, Lamela coming agonisingly close when his curling effort rattled the woodwork.
Then came Kane's moment of misfortune as Sunderland drew level against the run of play, and they could even have won it, Buckley turning a glorious chance just wide of the post late on.
