Only 146 seconds separated Alli's second-half opener and Kane converting from the penalty spot as Spurs moved 17 points clear of the Gunners and made it mathematically impossible for their rivals to close the gap.
Victory was only tarnished by Chelsea's emphatic 3-0 win at Everton earlier in the day, which means Tottenham could only reduce the difference at the top back to four points.
Relive the action on Standard Sport's live blog!
Tottenham: Lloris, Trippier, Alderweireld, Vertonghen, Davies, Dier, Wanyama, Eriksen, Alli, Son, Kane.
Subs: Walker, Janssen, Vorm, Nkoudou, Sissoko, Dembele, Wimmer.
Arsenal: Cech, Gabriel, Koscielny, Monreal, Oxlade-Chamberlain, Xhaka, Ramsey, Gibbs, Ozil, Sanchez, Giroud.
Subs: Ospina, Walcott, Holding, Iwobi, Welbeck, Bellerin, Coquelin.
Referee: Michael Oliver (Northumberland)
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WHAT THEY SAID
Mauricio Pochettino: "We have our own philosophy, our own titles, our own way and it is important now to be focused.
"I understand for the fans it means a lot, all that has happened with Arsenal, but my responsibility and for the players and the club is to try to win and win every game.
"I can understand because after 20 years Tottenham always was below Arsenal and I can understand that means a lot to be above but personally for me I want to be above Arsenal but I want to win the title more."
Arsene Wenger: "Let's be honest, I've answered that question about a shift in power over [many] years. Nothing changes in that.
"Do Spurs have to do more over a long period of time? I think so. You cannot say that the weight of one year has the weight of 20.
"For the pride and the continuity or our achievements, yes we want to fight to be in front of Spurs. [But] we have to focus on what is really important to us at this moment, which is to finish in the top four."