Mauricio Pochettino's side are now 17 points clear of the Gunners and mathematically assured of finishing above their rivals for the first time since 1995.
Spurs' ninth consecutive Premier League victory may not have been enough to put a significant dent in the lead of pacesetters Chelsea, who beat Everton earlier on Sunday afternoon, but few occasions will be sweeter than finally climbing out of Arsenal's shadow.
It all unravelled for Arsene Wenger's men in the space of three second-half minutes as Alli bundled home a fortuitous rebound while Kane rifled home from the penalty spot after being fouled by Gabriel Paulista.
The mood in N17 was jubilant at full time yet there was a nervousness lurking beneath the surface early on, typified by Jan Vertonghen's careless pass straight out for a throw-in.
More sloppy play led to Arsenal's first opportunity of the game when Kieran Gibbs was played in behind after Spurs were forced into a mistake inside their own half, but Hugo Lloris raced off his line to beat the Englishman to the ball.
Then two chances in as many minutes went begging for the hosts. Alli's composure failed him when he was picked out at the back post while Christian Eriksen could only find the top of the crossbar after Heung-min Son's shot deflected straight into his path.
The Gunners were struggling to create chances but Aaron Ramsey almost gave his side the lead against the run of play courtesy of a low effort that forced Lloris into a smart stop down to his left.
The visitors went close again when Alexis Sanchez's curling strike flashed just wide of the far post while a full-stretch Petr Cech kept out Vertonghen's long-range effort on the stroke of break.
The Arsenal goalkeeper was called into action moments into the second half too and showed superb athleticism to back pedal before tipping Victor Wanyama's looping strike over the crossbar.
Kane tried his luck from distance while Olivier Giroud, who cut an isolated figure up front throughout, rifled a volley wide of the mark.
The breakthrough arrived when Alli combined with Eriksen before the Dane's low effort was kept out by Cech. Three Arsenal defenders were slow to react but Alli pounced to poke home his 17th top-flight goal of the season.
The 21-year-old's strike put the wind in Spurs' sails and Gabriel buckled under the pressure when he dangled out a leg and felled Kane inside the area.
Referee Michael Oliver pointed to the spot and Kane picked himself up before coolly stroking the ball past Cech to send the Spurs faithful into raptures.
Spurs could have had another penalty when Sanchez appeared to handle Son's attempt to flick the ball over his opponent's head while Cech kept his side in it by keeping out both Vertonghen and Toby Alderweireld.
Pochettino's side - and the home crowd - savoured the closing stages with Arsenal unable to muster up a hint of a comeback.
'North London is ours' came the cry from the Spurs faithful and while perhaps it is too early to suggest a significant power shift is taking place no-one can deny the winds of change are certainly blowing in the capital.