Williams had taken just one point from their previous seven races and were last in the standings but Albon's six-point haul lifted the former champions above AlphaTauri and only a point behind Haas.
Even Red Bull boss Christian Horner, with Max Verstappen heading for that team's 100th win to continue their 100% winning record for the season, confessed he had been gripped by his former driver's exploits.
"Congrats to him. I ended up watching as much of his race as our race. He seemed to have half the field behind him," said the Briton.
On Saturday, when Albon posted the fastest lap in the second phase of a rain-hit qualifying, it looked like that might be as good as it was going to get.
The Thai had qualified 10th and started ninth but with two Ferraris and a Red Bull behind him had little real hope of scoring big points.
A one-stop strategy, with Albon completing 59 laps on a set of hard tyres and defending tenaciously, paid dividends for a team who started the weekend with new boss James Vowles discussing candidly how long it would take to catch up.
"Its not fun to drive around on old tyres but we made it work," said Albon, who led around a train of rivals for lap after lap before taking the chequered flag with his best result yet for the team.
"The tyres were lasting, they were staying cool, I could afford to push on them... the tyre deg (wear) was OK and we were just quick enough to stay in front."
Albon, voted Driver of the Day, told Sky Sports that the team had done an amazing job by rushing through aerodynamic upgrades.
"Two weeks ago we were at the factory and I was with James and I don't want to call it a crisis mode but we were so low on parts we actually fast-forwarded the upgrade because there was no point building the old car again," he said.
"I actually felt a bit of pressure because I was like ‘My god, they’re really putting everything into this weekend. And its all on my car. Don’t crash it and try and survive'. I'm just so happy we got points."
