Frank Lampard's side showed a very good football having up to 90% of ball possession.
However, Aston Villa were the first to score in the first half with a shot from Kourtney Hause after poor defending from the blues.
Substitute Christian Pulisic came off the bench and leveled the match in the second half before Olivier Giroud's winner after his shot was deflected at the back of the net.
This win increases Chelsea's hope of securing a spot for the champion league.
Chelsea are currently in 4th position with 51 points after playing 30 games.
Aston Villa are in 19th position with only 26 points after playing 30 game and are at risk of being relegated with only 8 matches to the end of the league.
Chelsea will be hosting Manchester city on Wednesday 24th June while Aston Villa will be visiting Newcastle on the same match day.
In other premier league match played on Sunday, league leaders Liverpool were forced to a draw against Everton at the Goodison park.
The much anticipated derby ended in a goalless draw in their fast match returning from the Corona pandemic break.
Liverpool are currently at the top of the league with 83 points after playing 30 matches.
They are 23 points away from second placed Manchester city and only need 5 points to be declared champions.
Klopp's men will be hosting Crystal palace on Wednesday in their next fixture while Everton will be traveling to Norwich city on the same match day.
Everton are currently in 12th position having 38 points after 30 games played.