The win was Liverpool’s first in four Premier League games take them up to seventh place in the table with 11 points.
The Germany international was moved out of midfield back into defence where he spent the majority of last season playing.
Daniel Sturridge returned from injury for the home side to score a brace while James Milner scored the Red’s remaining goal.
Summer signing Gestede struck twice for the visitors midway though the second half.
Liverpool take on Sion in the Europa League during the week and take on their rivals Everton in the Premier League next weekend.
Liverpool v Aston Villa
Kick-Off: 15:00 GMT
Liverpool starting lineup:
Mignolet, Clyne, Skrtel, Sakho, Moreno, Can, Lucas, Milner, Coutinho, Ings, Sturridge
Subs: Bogdan, Toure, Gomez, Lallana, Allen, Origi, Ibe
Aston Villa starting lineup:
Guzan, Hutton, Richards, Clark, Amavi, Westwood, Grealish, Veretout, Ayew, Sinclair, Gestede