Mohamed Salah and Virgil van Dijk both struck in the opening half for the Reds, while Ollie Watkins pulled a goal back for the hosts after the interval.
But the visitors sealed three points in the final 10 minutes of the contest through substitute Stefan Bajcetic, who netted his first senior goal for Jürgen Klopp's side.
Team news
The Reds made six changes for the trip to Villa Park, with Alisson Becker starting in goal while Trent Alexander-Arnold and Van Dijk were selected in defence.
Skipper Jordan Henderson and Fabinho came into midfield, with Alex Oxlade-Chamberlain joining the attack.
Liverpool: Alisson, Alexander-Arnold (Gomez, 79), Matip, Van Dijk, Robertson, Fabinho, Thiago (Keita, 66), Henderson (Bajcetic, 78), Oxlade-Chamberlain (Elliott, 66), Salah, Nunez (Doak, 87).
Subs not used: Kelleher, Tsimikas, Carvalho, Phillips.
First half
It was Liverpool who struck first thanks to a clever move that opened up the hosts' defence in just the fifth minute of the match.
Alexander-Arnold's second ball following a clearance at a corner found fellow full-back Andy Robertson inside the area, with the Scotland international playing a first-time low cross into the path of Salah.
The No.11 timed his run into the six-yard box and made no mistake to find the back of the net and put the Reds into the lead.
Unai Emery's men attempted to respond, forcing Alisson into a number of saves, with Watkins' back-post header the most notable of chances.
The Reds were denied a second on the 20-minute mark, with Joel Matip seeing a guided header from a Robertson free-kick settle into the back of the net, though an offside flag intervened.
Darwin Nunez then went close on two occasions, first heading over the crossbar before volleying into Robin Olsen's legs following a swift flurry forward after a Villa attack.
Liverpool, however, added to the scoreline ahead of the half-time break as Van Dijk struck from inside the area after Salah kept the ball alive at a corner.
The centre-back's low effort took a slight deflection from retreating Ezri Konsa to hand the Reds a deserved cushion at the interval.
Second half
Following the break, Villa thought they had found a way back into the contest almost immediately as Watkins raced through on goal to find the bottom corner.
An offside flag, though, halted celebrations with VAR confirming the decision to rule out the goal.
Defender Lucas Digne also went close for the home side, while Salah and Fabinho both saw efforts fall the wrong side of the post.
Before the hour mark, Watkins did get himself on the scoresheet as he found space inside the area to head home and reduce the deficit.
Villa attempted to apply pressure in their search for a leveller, while the Reds defended resolutely, threatening on the break.
Nunez struck narrowly wide at pace on one counter, while he brilliantly kept the ball in play to help restore the two-goal advantage.
The forward raced to the byline and pulled the ball back into the area, where substitute Bajcetic was waiting to coolly slot home.
The goal was enough to secure three points and cap a winning return to Premier League action for Liverpool.