What you need to know:
- Kane towered above the Arsenal defence to head home his 32nd goal of the season four minutes into the second half.
- Victory moved Spurs up to third above Liverpool and Chelsea, while sixth-placed Arsenal now lie six points off the top four.
Sergio Aguero scored four second-half goals as Manchester City's march towards the Premier League title continued unabated with a 5-1 thrashing of Leicester on Saturday to move 16 points clear of Manchester United.
Aguero now trails Harry Kane by just two goals in the race for the golden boot, but just one from Kane was enough to win the North London derby as the Tottenham striker's seventh goal in as many games against Arsenal secured a 1-0 win.
Riyad Mahrez made his Leicester return after ending his self-imposed exile at protest after the Foxes turned down a transfer deadline day advance by City for the Algerian.
However, the damage had already been done for the visitors by the time Mahrez entered as a substitute just after the hour mark thanks to another Aguero masterclass.
Kevin De Bruyne's teasing low cross was turned home by Sterling for his 20th goal of the season inside three minutes, but there was a rude awakening for City's record signing Aymeric Laporte on just his second appearance for the club as Jamie Vardy skipped beyond the £57 million defender before his deflected shot found the bottom corner.
Leicester were powerless to stop Aguero after the break as the Argentine took advantage of two more wonderful De Bruyne passes and then an errant clearance from Leicester 'keeper Kasper Schmeichel to complete his hat-trick.
The best was yet to come as Aguero smashed a 20-yard drive in off the underside of the bar.
Kane towered above the Arsenal defence to head home his 32nd goal of the season four minutes into the second half, as only some wayward finishing and stunning goalkeeping from Petr Cech saved the visitors from further embarrassment in front of a Premier League record crowd of 83,222 at Wembley.
"He is the present and the future," Mauricio Pochettino said when quizzed whether Kane's dominant header possessed traits of an old-fashioned English centre-forward.
"It is amazing all that he is achieving, (I'm) so proud and happy he is in our side."
Victory moved Spurs up to third above Liverpool and Chelsea, while sixth-placed Arsenal now lie six points off the top four.
And more questions will be asked of Alexandre Lacazette's future role at the Emirates in the wake of Pierre-Emerick Aubameyang's arrival as the Frenchman missed a great late chance to snatch a point after coming off the bench.
"Kane made the difference, that is what he is about," Arsenal boss Arsene Wenger said.
"Once they scored you could see we were wobbling for a while and they could have scored one or two more, but in the last 10 minutes we should have come back to 1-1."
Kane spoke this week of how being released from Arsenal's academy as an eight-year-old left him with a "chip on his shoulder".
The man now christened 'one of their own' by the Spurs faithful hasn't let Arsenal forget that decision as he powered Ben Davies' cross into the bottom corner.
At the other end of the table, Swansea's stunning revival under Carlos Carvalhal continued as Ki Sung-Yueng's fine strike nine minutes from time earned a 1-0 win over Burnley to moved up to 14th.
West Ham also eased their relegation fears as goals in either half from Javier Hernandez and Marko Arnautovic ensured they moved five points clear of the relegation zone with a 2-0 win over Watford.
Stoke remain in the bottom three as Charlie Adam saw a stoppage-time penalty saved in a 1-1 draw against Brighton, while Everton eased past Crystal Palace 3-1.