Arsenal - without injured striker Alexis Sanchez - were on course for their first back-to-back victories at Spurs since the late 1980s after taking the lead in Arsene Wenger's 700th Premier League game in charge.
However, Kane - rewarded with a bumper contract at the beginning of the week - had other ideas as he turned the game on its head following Mesut Ozil's opener to give Spurs a first derby win in five attempts.
Despite the hosts making the early running, the in-form Ozil opened the scoring 11 minutes in after an incisive break, with Spurs initially frustrated in their attempts to get back on level terms.
Tottenham's pressure eventually told when Kane grabbed his first derby goal to level in the 56th minute, and the England under-21 international took his tally to 11 goals from his last 14 Spurs appearances late on with a superb header.
Arsenal's five-match winning run in all competitions therefore came to an end, Tottenham leapfrogging their rivals into the top four.
Tottenham edged a cagey opening, with David Ospina forced to tip Kane's early effort wide before the Colombian easily collected Danny Rose's disappointing delivery from the left.
However, in Arsenal's first purposeful foray forward, the recalled Danny Welbeck burst past a surprisingly sluggish Rose to square for Olivier Giroud in the centre.
The Frenchman cleverly helped the ball onto Ozil, with the Germany international able to angle his body and volley past Hugo Lloris to score for a third game running.
An increased intensity from both sides saw chances flow before the half-hour mark, with Rose threatening Ospina's goal twice more down the left.
However, the Arsenal defence stood firm to soak up Spurs' pressure - wasteful finishing from Christian Eriksen and Ryan Mason helping their opponents' cause.
Welbeck was required to clear Eriksen's dangerous free-kick late in the first half and Spurs started the brighter after the break.
A lack of cutting edge in the final third continued to prove their downfall until Kane drew his side level with a cool finish at the back post after Ospina had failed to palm Erik Lamela's corner out of danger.
The goal was no more than Spurs' pressure deserved but Welbeck almost put Arsenal back in front soon after - his curling effort kept out at full stretch by Lloris.
Ospina was called on again to deny Kane - having initially saved from Nabil Bentaleb - but the 21-year-old would not be denied as he further cemented his status as Spurs' latest fan favourite.
Kane's 22nd goal in all competitions came courtesy of a wonderful arching header from Bentaleb's cross as the striker impressed again in front of watching England manager Roy Hodgson.
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