Spurs were twice kept at bay by the woodwork – Kane and Erik Lamela the players denied – before opening the scoring.
But Kane netted on the stroke of half-time and wrapped up a comfortable triumph three minutes after the interval, both set up by England team-mate Dele Alli.
Having lost ground in the title race with defeat at West Ham and a north-London derby draw against 10-man Arsenal earlier this month, followed by a 3-0 Europa League thrashing at Borussia Dortmund, Mauricio Pochettino’s men needed a lift.
And they could not have wished for better opponents than the beleaguered Villa, who appear as good as relegated after a fifth loss on the spin.
Protests by the home supporters were called off after the club announced the arrivals of popular former player and manager Brian Little and ex-Football Association chairman David Bernstein to the board this week.
But still, there was little for the locals to cheer about as Spurs dominated from kick-off.
Chance after chance went begging before Kane finally broke the deadlock.
He struck the crossbar in the third minute after latching onto Lamela’s through-ball and also wasted other good opportunities.
Brad Guzan must have thought it was his lucky day as the England striker shot straight at him from eight yards out after good work from Danny Rose down the left.
Then, when Jores Okore mis-timed a tackle, Kane ran at goal from a tight angle but once again fired into the United States international’s hands.
The goals were never far away, though, despite further off-target shooting from the visitors.
Kyle Walker, who got the better of Aly Cissokho all afternoon, crossed for Lamela but the woodwork saved Villa for a second time when the attacker’s shot crashed off the post.
But, given his previous joy against the claret and blues, it was no surprise to see Kane fire Spurs ahead.
Alli was fouled midway in the Villa half and, while the hosts switched off, the young midfielder’s quickly taken free-kick played in the forward, who fired past Guzan.
The same pair combined for the second as Alli broke free down the left and crossed for Kane, who made no mistake with the finish within three minutes of the restart.
It was his fourth goal in as many games against Villa, and the third time in four encounters that Villa had conceded in the first five minutes of the second half.
Manager Remi Garde’s face – like thunder – explained exactly how he felt about it, while Pochettino looked pleased with another impressive away performance, and more importantly the three points that kept the heat on the Foxes.
At 2-0 his side were content to keep possession and see out the game despite a number of late chances from Villa.
Rudy Gestede smashed the crossbar from close range and Joleon Lescott screwed wide from two yards, but the outcome was never in doubt.