The South Korea forward cashed in on Bjorn Engels' stoppage-time error to snatch the three points for Jose Mourinho's side after Engels' 53rd-minute header had looked like earning Villa a priceless point in their fight against relegation.
Dan Kilpatrick was at Villa Park to assess the key talking points...
Chaos reigns at Villa Park
After scarcely-deserved victories over Manchester City and Southampton, Tottenham's winning streak continued with a 3-2 victory at Villa Park, thanks to Heung-min Son's dramatic stoppage-time winner.
The visitors had more than enough chances to win before the South Korean capitalised on Bjorn Engels' error to slide under Pepe Reina.
But they rode their luck at times and were lucky not to be more than one goal down after Toby Alderweireld’s early own goal. The victory continued a pattern of playing below-par but eking out impressive results under Jose Mourinho.
More than anyone, Son seems to typify Spurs at the moment, having now scored six times in five games, despite not being close to his electrifying best.
Jose Mourinho's side are clearly missing injured talisman Harry Kane but they are also relying on luck and chaos to a degree – a risky long-term strategy.
With every goal here, the narrative seemed to change. Spurs were shambolic, then fortuitous. They were steely, then careless. And then finally clinical. Whatever the case, winning while not playing well is the sign of a great team, apparently, but it feels like Tottenham’s luck will run out eventually.
While this was a big win in the race for fourth (or fifth), they surely cannot be so scatty in Wednesday's Champions League clash with RB Leipzig.
Dier off the pace on return
Mourinho left nearly £100million-worth of midfield talent on the bench in Tanguy Ndombele and Giovani Lo Celso in favour of Eric Dier, who started for the first time in the League since the defeat to Chelsea before Christmas.
His return was presumably with two factors in mind: Wednesday's Champions League clash with RB Leipzig and the threat of Jack Grealish, who operated from the left of Villa's front three again.
After just about making it to half-time against Chelsea, Dier managed an hour here before he was hooked for Giovani Lo Celso after another off-the-pace performance. While tidy in possession, Dier simply looked incapable of performing his primary role of shielding the back four from the likes of Grealish and Anwar El Ghazi, who both ghosted past him on at least one occasion.
It was no surprise that Spurs looked far better with the introduction of Lo Celso. Mourinho will argue that he had little choice but to rotate given the fixture pile-up but, for the moment, Dier feels like a passenger that this Spurs side can ill-afford to carry.
Spurs' Mr. Consistent turns jittery
No-one in the Spurs XI will have been more relieved by Son's last-minute winner than Toby Alderweireld, who was at fault for both Villa goals.
The Belgian was uncharacteristically jittery from an Anwar El Ghazi cross to turn the ball into his own net, although he surely expected Hugo Lloris to be more assertive, before he was beaten by Engels at a corner for Villa's second.
In between, he made amends with a brilliant finish into the roof of the net on the turn but it is his poor defending which was most notable.
Alderweireld has the excuse of some sleepless nights after his wife gave birth to their second child on Friday but he fell below his usual high and consistent standards here.
A blip is understandable but Alderweireld has been Tottenham's most consistent defender for most of this season and a dip in his form would be a major concern for Mourinho given the other problems at the back.