A deserved victory kept them four points behind leaders Chelsea, who won 3-0 at Everton earlier.
Alli put Spurs ahead in the 56th minute when he followed up after Christian Eriksen's shot was saved. Two minutes later Kane went down in the penalty area under Gabriel's challenge and got up to convert the penalty.
Tottenham's victory in Arsene Wenger's 50th North London derby as Arsenal manager ensured Spurs will finish above their neighbours for the first time in 22 years.
It was their ninth successive league win and the margin would have been greater but for some fine saves by Petr Cech.
A disappointing Arsenal were restricted to a single chance in the first half when Aaron Ramsey brought a good low save from Hugo Lloris shortly before halftime.
Spurs in contrast were guilty of two bad misses. Midway through the half Kane's effort was deflected to the far post where Alli could only head wide.
Three minutes later Eriksen clipped the bar as another deflection reached him just a few metres out.
Cech was much the busier goalkeeper, making saves either side of the interval from Jan Vertonghen and then Victor Wanyama.
He then kept out a close-range effort from Eriksen but could not prevent Alli driving in the opening goal.
In the next attack Kane won and converted the penalty to leave Arsenal wilting.
The visitors exerted some late pressure but never looked like threatening Mauricio Pochettino's side and remain in danger of missing out on a Champions League place for the first time under Wenger.
(Reporting by Steve Tongue; Editing by Ken Ferris)
Share
