Aston Villa fought hard before succumbing to two second half strikes against the Premier League champions at Anfield.
The visitors had the better of the first half and were probing for the opener before Sadio Mane intervened after 70 minutes.
The Senegalese winger crashed the ball home as the Reds took one of the few chances that they created against a stubborn Villa side.
Substitute Curtis Jones put the finishing touches on their victory a minute from time as Liverpool continued their 100% record on home turf this season.
Defeat leaves the Villans in 18th place in the table, one point adrift of Premier League safety.
Dean Smith made five changes – Matt Targett’s absence enforced through injury – from the team that lost 1-0 to Wolves last weekend, bringing in John McGinn, Neil Taylor, Anwar El Ghazi, Trezeguet and Pepe Reina as he reverted to a 4-3-3 formation.
The changes saw Villa match their opponents man for man across the pitch as they stifled Liverpool, and by the time the teams headed off for the first drinks break, Ezri Konsa’s wayward header was the only effort at goal from either side.
It took until the 33rd minute for a goalkeeper to be called into action, with Alisson making a routine stop from Douglas Luiz’s vicious half-volley.
The champions, fresh from a 4-0 humbling against Manchester City in midweek, lacked urgency but with Mohamed Salah, Mane and Divock Origi leading the line, they carried a threat that ensured Villa had to be on their guard at all times.
Salah drifted into the box and forced Reina into a comfortable save at his near post after 37 minutes in what amounted to the hosts’ only effort on goal of the first half.
As the second half began, Villa were finding success on the counter-attack and when Jack Grealish marauded through the middle, he found himself with El Ghazi and Keinan Davis making runs either side of him.
The captain opted to slide in El Ghazi, whose fierce first-time drive forced Alisson into a smart reaction stop.
Jurgen Klopp introduced Jordan Henderson, Roberto Firmino and Georginio Wijnaldum from the bench in a bid to lift his off-colour team, but it took until the 70th minute before the finally clicked into gear.
The opening goal was simple in its creation, with Naby Keita receiving a pass on the corner of the box before threading a pinpoint ball through to Mane, who crashed a shot in off the underside of the crossbar.
Buoyed by the opener, the home side proceeded to dominate possession before substitute Jones rounded off proceedings in the final moments.
The young midfielder beating Reina from close range with the help of a deflection.
Villa: Reina, Konsa, Mings, Hause, Taylor, McGinn, Luiz, Trezeguet (Vassilev 84), Grealish (c), Davis (Samatta 74), El Ghazi (Jota 74).
Subs: Nyland, Lansbury, Elmohamady, Nakamba, Hourihane, Guilbert.