Alli, scorer of a goal-of-the-season contender in his last outing at Crystal Palace, put Tottenham ahead from close range after two minutes and was then fouled in the area by Sebastien Bassong, allowing Kane to stroke home a penalty.
Kane, who was twice denied by the woodwork, then took his league tally for the season to 15, all in his last 18 games, with a cool finish in the dying minutes as Tottenham leapfrogged North London rivals Arsenal into third place.
"It was an excellent performance, I'm very pleased," coach Mauricio Pochettino told reporters. "The effort was fantastic.
"The early goal helped us and in the end we deserved the result and we need to feel proud of the players for the job they did. The performance was fantastic from the beginning."
The only worrying moment for Tottenham's travelling fans was the sight of 19-year-old Alli being substituted shortly after halftime.
"He was a little dizzy, he felt unwell and with advice from the doctor we took the decision to substitute him for Nacer Chadli," Pochettino said.
"It's always better not to take a risk but now he feels much better. It's not a serious problem."
Tottenham host Watford on Saturday.
(Reporting by Martyn Herman; editing by Toby Davis/Peter Rutherford)
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