Both Liverpool's goals came from set pieces.
Craig Bellamy put Liverpool ahead in the 11th after Villa failed to clear a corner kick, poking in from close range after the ball had hit goalkeeper Brad Guzan.
Bellamy then took a powerfully struck corner from the left, sending the ball onto Martin Skrtel's head for the unmarked defender to score.
Kenny Dalglish's first league win as a manager at Villa Park took Liverpool to 29 points from 16 games, 10 more than mid-table Villa.
Liverpool could have won by more against a poor Villa side that showed little attacking threat without the suspended Gabriel Agbonlahor and England striker Darren Bent, who was ruled out because of a thigh injury.
Luis Suarez, who tormented the Villa defense and twice hit the frame of the goal before he was substituted on 74 minutes, received an ovation from the visiting fans as he was replaced by Andy Carroll.