Kane broke the deadlock just before halftime with an angled finish from a free kick taken by Delle Ali. The England forward struck again just three minutes after the restart at Villa Park, again being set up by Ali.
It was Kane's 19th league goal of the season, drawing him level with Jamie Vardy of Leicester in the list of top-scorers and ensuring Spurs finished the day with 58 points from 30 games.
Surprise leader Leicester has 60 points from 29 matches.
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