A third consecutive Premier League victory lifts Spurs up to fifth - which could be enough to secure Champions League qualification with Manchester City facing a two-season ban from the competition - and within one point of fourth-placed Chelsea.
José Mourinho's men were worthy of their victory after bouncing back from a nightmare start when Toby Alderweireld sliced into his own goal.
The Belgian quickly made amends at the other end with a thumping finish before Son followed up after Pepe Reina had saved his penalty to put the visitors in front.
Slack defending threatened to cost Tottenham all three points when they allowed Bjorn Engels to equalise early in the second half.
However, Engels was the culprit to cost Villa a point in their battle to beat the drop as he miscontrolled a long ball forward in the 94th minute and Son sprinted clear to finish calmly.