Ollie Watkins' only previous goals this season had come in a hat-trick at Hibernian in the Europa Conference League qualifying round
Ollie Watkins fired home an unerring winner between the legs of Robert Sanchez from an incredibly tight angle as Villa capitalised on Malo Gusto's dismissal for dangerous play.
Mauricio Pochettino's hosts fashioned plenty of chances before Gusto's red card for a poorly-timed tackle that caught Lucas Digne on the ankle but, as so often this season, failed to take any of them.
Nicolas Jackson and Raheem Sterling were both denied one-on-one by excellent Emiliano Martinez saves while Enzo Fernandez sliced another glorious opportunity wide.
Chelsea had been equally indebted to their own goalkeeper as Sanchez made a pair of flying fingertip saves to thwart beautifully-struck volleys by Digne and Nicolo Zaniolo.
There were chances at both ends even after Gusto was sent off but Villa, who climb to sixth, took one of theirs via Watkins, while Chelsea failed to score for a third successive game to stay 14th.
The Blues have just five points from their opening six games and their woes pre-date Pochettino's appointment, with only two wins and 11 goals in their past 14 home league matches.
But the Argentine remains convinced better times lurk just around the corner if his side can overcome their shyness in front of goal.
"The team never gives up and of course we are going to fight to change as quickly as possible," he said.
"I am seeing the team trying. We created many chances. We cannot criticise or say anything about the capacity to fight, they are fighting and they have the will."
-- Courtesy of BBC Sport