The Reds were dominant in the first half but they were met by a strong Aston Villa defence who limited their threat as the two sides went level into the break.
Jurgen Klopp's side upped the ante in the second half and they took the lead with a little over 20 minutes left as Tyrone Mings brought down Mohamed Salah inside the box, with the Egyptian converting from the spot-kick to give Liverpool the lead.
Liverpool squandered chances to double their lead as the visitors felt increasingly encouraged in spells. Despite a nervy ending to the game, the Reds ultimately saw out a 1-0 win to keep pace with their fellow title rivals.
Klopp made seven changes to the makeshift side from midweek, with the likes of Trent Alexander-Arnold, Virgil van Dijk, Thiago and Jordan Henderson all returning to the starting eleven. Alex Oxlade-Chamberlain started in the front three, with Diogo Jota on the bench.
There was a warm welcome for club legend and now Aston Villa manager Steven Gerrard, but once the pleasantries were over, it was all business as Liverpool looked to make a lively start to the game.
Sadio Mane saw an early shout for a penalty turned down before an excellent move saw Mohamed Salah dummy the ball and allow the ball to run into the path of Alexander-Arnold, whose shot was deflected over the crossbar by Matt Targett.
Thiago dictated much of the proceedings for Liverpool in the middle of the park and his ball forward gave Oxlade-Chamberlain the chance to unleash from the outside of the box, but the midfielder's effort went inches over the woodwork.
An incisive ball by Mane slid Robertson down the left and into the box before Marvelous Nakamba brought him down inside the box, but neither the referee nor VAR were interested in the challenge.
A moment of hesitance by Alisson, combined with a slip on the wet Anfield pitch, gave Ashley Young the opportunity to take advantage but Joel Matip was on hand to stop the danger.
Liverpool's threat and possession continued to increase as the half wore on, but the visitors stood up rigidly in defence and looked to keep the Reds away from the vicinity of the goal.
Mane and Robertson combined down the left as the latter evaded the oncoming Emi Martinez and pulled the ball back in search of a Reds shirt, but it was cleared to safety with relative ease for the visitors.
Salah was thwarted well for most of the first half but the Egyptian made a yard of space for himself inside the box as he sent a powerful low drive towards the near post just before the break, but Martinez was up to the task as he got down and denied the Reds forward.
The second half started much the same as the first, with the Reds continuing to be left frustrated by a well-drilled Villa defence as Robertson's pull-back towards Salah was thwarted by a Tyrone Mings interception.
Liverpool's best opportunity of the game thus far came through a Virgil van Dijk header, with the Dutchman pulling away from the pack from a Robertson corner and getting a powerful header on target, but Martinez anticipated well as he pushed the ball over the crossbar.
The Reds continued to mount pressure on the visitors' defence as Klopp looked to further turn the screw with Oxlade-Chamberlain making way for Diogo Jota.
A lofted cross by Mane was controlled by Salah, who ignored Alexander-Arnold on the overlap and sent a curling strike at goal, but the Reds' No.11 was unable to find the target.
Liverpool's dominance eventually paid off as Salah looked to burst part Mings inside the box, with the Villa centre-back bringing him down and referee Stuart Attwell awarding the spot-kick.
Salah made no mistake from 12 yards out as he pinged his penalty into the bottom right corner in front of the Kop to mark his 21st goal of the season and give Liverpool a well-deserved 1-0 lead.
Former Liverpool striker Danny Ings' introduction soon thereafter gave Villa a new dynamic in attack as the visitors enjoyed a rare prolonged spell in Liverpool's third, with the Reds having to dig deep and defend well.
A quick counter-attack should have given Liverpool the opportunity to double their lead as Mane slid Salah through on goal, but he chose to find the reverse ball instead of taking the shot as the chance was smothered.
James Milner and Takumi Minamino came on in the closing stages as the Anfield crowd grew increasingly anxious in the final minutes, with Liverpool continuing to look to press high and restrict any developing moves.
A combination of Salah and Jota looked to add a late goal to consolidate their lead but it wasn't to be as it ultimately finished 1-0 to the Reds.
Liverpool: Alisson, Alexander-Arnold, Matip, Van Dijk, Robertson, Fabinho, Thiago, Henderson, Salah, Oxlade-Chamberlain, Mane
Aston Villa: Martinez, Cash, Konsa, Mings, Targett, McGinn, Nakamba, D Luiz, Ramsey, Watkins, Young
MOTM: Joel Matip