Daniel Sturridge scored the only goal of the game at Villa Park to give the Merseysiders the three points.
Villa enjoyed a difficult first 45 minutes, but a spirited second-half display saw them nearly snatch a point.
Here, Sports Mole's assesses the action between the two sides.
On target 3
On target 1
Was the result fair?
It was a real game of two halves at Villa Park as Liverpool dominated the opening 45 minutes, while the hosts pushed hard during the second period. A draw would not have been an unfair result, although it was the visitors who showed a more ruthless streak to come away with the spoils.
Aston Villa's performance
Paul Lambert's side looked toothless for most of the first half, but they were much improved after the break. There was a lot of energy in midfield, and Christian Benteke may have bagged himself a couple of goals on another day. However, they ultimately came up short against a dogged Liverpool side.
The Merseysiders were utterly dominant for the opening 45 minutes, passing the ball around with plenty of purpose. They were pinned back in their own half for much of the second half, but that gave them the chance to demonstrate how difficult they are to break down with a courageous defensive display.
Sports Mole's man of the match
Steven Gerrard: The Liverpool captain was an integral part of his team going forward in the first half and also put in an extremely determined display in front of his back four late on as Villa cranked up the pressure. This was the type of all-round display that the midfielder has made his trademark down the years.
Villa had the chance to ask a question of the Liverpool defence late on when they won a free kick out wide, but substitute Aleksandar Tonev decided to go for goal from an improbable angle, smashing the ball well wide.
Mark Clattenburg brandished a number of yellow cards throughout the contest, but overall the official made more right decisions than wrong and helped to keep the game flowing.
Aston Villa: The Villans return to action on Tuesday when they travel to Rotherham United in round two of the Capital One Cup.
Liverpool: The Reds get their Capital One Cup campaign underway on Tuesday with a home tie against Notts County.