Spurs were on course for a Premier League opening day shock for 73 minutes as they trailed to John McGinn’s early opener.
However, club-record signing Tanguy Ndombele sparked the fightback by curling home from distance to level before Kane struck twice in the final four minutes.
Villa spent over £100 million ($120 million) on 12 new recruits over the summer to try and stabilise themselves as a Premier League force again after three seasons in the second tier.
And there were plenty of promising signs for Dean Smith’s men, particularly in the first 45 minutes, before they wilted under Spurs’ relentless second-half pressure.
Despite a host of new arrivals, it was one of Villa’s heroes in gaining promotion from the Championship last season who stunned Mauricio Pochettino’s men early on.
From a long ball forward, Wesley outmuscled Davinson Sanchez to allow McGinn to burst through and he kept a cool head to leave Danny Rose on the floor before firing into the bottom corner.
The visitors could even have been further ahead had one of their new recruits Trezeguet been more clinical at the end of a couple of promising counter-attacks.
Spurs soon had the visitors penned in, though, as Kane headed over then fired wide when one-on-one with Tom Heaton as half-time approached.
The pressure continued to build on the Villa goal after the break, but Spurs were often too wasteful to take advantage as Moussa Sissoko dragged horribly wide with just Heaton to beat.
Christian Eriksen had been left on the bench with doubts remaining over the Dane’s future with the transfer market across Europe still open until September 2.
Pochettino finally called for his ability to pick the lock of a packed defence 25 minutes from time.
Eriksen certainly did not appear lacking in commitment as he immediately offered the cutting edge Spurs had lacked.
Heaton made a stunning save as Sanchez turned Eriksen’s cross goalwards 17 minutes from time, but the rebound was worked back to Ndombele who curled home from the edge of the area.
Only another brilliant save from Heaton denied Eriksen scoring moments later with a thumping strike from a free-kick.
However, Heaton was helpless four minutes from time when the ball broke Kane’s way and the England captain hammered the ball home to break his duck at Tottenham’s new home.
