The result left Chelsea fourth on 51 points from 30 games, five ahead of fifth-placed Manchester United, while Villa’s hopes of avoiding the drop were dented as they stayed second-bottom on 26 points, one point adrift of the safety zone.
Chelsea boosted their hopes of securing Champions League football next season as second-half goals from Christian Pulisic and Olivier Giroud secured a 2-1 comeback win at relegation-threatened Aston Villa in the Premier League on Sunday.
The result left Chelsea fourth on 51 points from 30 games, five ahead of fifth-placed Manchester United, while Villa's hopes of avoiding the drop were dented as they stayed second-bottom on 26 points, one point adrift of the safety zone.
Substitute Pulisic equalised on the hour and Giroud netted the winner two minutes later after defender Kortney Hause had fired the home side ahead against the run of play in the 43rd minute with his first Premier League goal.
Hause achieved a rare accomplishment of scoring in each of England's top four divisions when he scrambled in a close-range rebound after Chelsea keeper Kepa Arrizabalaga parried an Anwar El Ghazi shot from a delightful cross by Douglas Luiz.
"We dominated, but it's the story of some of our games, we need to be more clinical," Chelsea manager Frank Lampard told Sky Sports. "But I can give the players some leeway because they've had a lot of time off. We showed great character and quality in the second half to win the game."
Chelsea had 76% of the possession in the opening half and missed a string of chances, with Villa keeper Oerjan Nyland twice denying Mason Mount while Mateo Kovacic volleyed inches wide from the edge of the penalty area.
Arrizabalaga was also forced into action at the other end when he parried a ferocious El Ghazi shot from 25 metres, while Ruben Loftus-Cheek failed to get a touch on Mount's low cross at the far post in the 39th minute.
American Pulisic equalised five minutes after coming on, when he stabbed a Cesar Azpilicueta cross off the underside of the bar at the far post as Villa's defence finally cracked under intense Chelsea pressure.
Azpilicueta delivered another telling assist two minutes later, threading the ball to Giroud from a flowing move and the Frenchman's deflected shot on the turn gave Nyland no chance.
Villa missed a gilt-edged chance to snatch a draw in the 87th minute when Spanish substitute Jota drove an opportunist shot inches wide of the far post after a sloppy clearance by Chelsea defender Andreas Christensen.