However, it was the visitors who took the lead in the ninth minute when Gabriel Agbonlahor poked home after a corner had fallen to him kindly inside the box.
They had the chance to double their lead four minutes later as Philippe Senderos got on the end of Ashley Westwood's free kick, but the defender could only guide his header over the bar.
The hosts struggled to create chances, but Adam Lallana came close to finding the net moments before half time when he fired a strike just wide of the post, before Mario Balotelli saw a powerful effort deflected over the bar.
After the break, Balotelli and Jordan Henderson both headed over as Liverpool pressed for a way back into the match.
Philippe Coutinho came within inches of equalising for the Reds as the game entered the final 10 minutes, but his curling effort came crashing back off the post, with Brad Guzan left stranded.
Liverpool laid siege to the Villa goal in the closing stages, but Paul Lambert's men managed to hold on and claim the win that extends their unbeaten run at Anfield to four seasons.