Reds midfielder James Milner opened the scoring after 66 seconds against his former club from 20 yards.
Striker Sturridge doubled their lead after the break with a volley following a one-two with Milner, but Rudy Gestede pulled one back from close range.
Watch All GOALS and Highlights: Liverpool 3-2 Aston Villa
Sturridge scored his second from Philippe Coutinho’s pass, but Gestede gave Villa hope with a fine header.
Liverpool boss Brendan Rodgers had been under pressure after six games without a win, other than Wednesday’s League Cup penalty shootout victory over Carlisle.