Villa looked on course for a third successive win after leading at the interval through Christian Benteke's 18th goal of the campaign.
Ashley Westwood's cross was turned back by Gabriel Agbonlahor to Benteke who drilled a fierce shot past Jose Reina who got a hand on the ball but could not keep it out of the net.
But the Reds equalised through Jordan Henderson early in the second period.
Philippe Coutinho's defence-splitting pass was seized on by Henderson who flicked the ball past Bard Guzan into the corner of the net for his fourth goal of the season.
Then skipper Steven Gerrard's penalty sealed victory for the visitors after Luis Suarez was brought down in the box by Nathan Baker and the resulting spot-kick .
The home side, who slipped into the relegation zone for the fifth time this season on Saturday, are level on points with Wigan but have an inferior goal difference.
Villa posed plenty of threat to Liverpool in the first half with Benteke and Agbonlahor linking well and Westwood pulling the strings in midfield.
But Liverpool upped their game a gear in the second period as they closed the gap on sixth-placed Everton to three points.
Luis Suarez was a handful throughout the 90 minutes, despite his World Cup qualifier exertions in Uruguay in midweek, and came close on several occasions to notching his 30th goal of the season.
- Sports & Recreation
- Gabriel Agbonlahor
- Christian Benteke
- Jordan Henderson