The two underperforming sides both enjoyed periods of possession and pressure in the first 45 minutes, but it was former Wolves man Diogo Jota who returned to haunt the West Midlands outfit as he broke the deadlock with virtually the last kick of the first half.
Wolves had a couple of penalty appeals waved away by referee Craig Pawson during the course of the game, and the hosts continued to huff and puff for an equaliser in the dying embers of the game, but there was no way through for the hosts as Mohamed Salah had a goal of his own ruled out for offside.
However, the result of the game was largely overshadowed by a nasty injury suffered to Wolves goalkeeper Rui Patricio in the second half, with the concussion substitutes rule being utilised as John Ruddy saw out the game for the hosts after a significant delay.
Liverpool's triumph on the Molineux turf propels them up to sixth in the table - above Tottenham Hotspur and Everton but still five points adrift of the Champions League places - while Wolves remain 13th on 35 points.
Wolves' first game back after the international break will be another home clash against top-four challengers West Ham United, while Liverpool face a daunting trip to Arsenal in the first weekend of April.
5th min: Traore feeds it through to Semedo on the right, and the full-back beats Andy Robertson before getting a left-footed shot away, which Alisson parries.
22nd min: Mane explodes down the left-hand side and gets away from Romain Saiss inside the area, but he cannot pick out a teammate in red.
38th min: Trent Alexander-Arnold manages to pick out Mane in acres of space in the Wolves box, but he is unable to direct his header on target.
43rd min: Wolves are awarded a free kick as Thiago is booked for a foul on Traore. Ruben Neves lines up one of his trademark long-range efforts, but it is not troubling Alisson.
45th min: Neves once again finds himself with the ball at his feet and attempts to pick out the far corner from the right-hand side, but fails to do so.
45th+2 min: Liverpool draw first blood on the stroke of half time. The Reds' attacking trio all combine as Diogo Jota hits it first time from the left, and while Patricio gets a hand to his effort, the former Wolves man marks his return to Molineux with the first goal on the night. 0-1 Liverpool.
49th min: Romain Saiss is allowed plenty of time to pick out Conor Coady in the Liverpool box, but the Wolves captain watches his header sail over the crossbar.
53rd min: Alexander-Arnold whips in a dangerous free kick towards the far post, and Ozan Kabak is inches away from getting his head to it.
64th min: Joao Moutinho is shoved over by Alexander-Arnold inside the area, but once again, Pawson waves away the protests.
73rd min: Phillips's attempted pass is intercepted and Traore attempts to beat Alisson with a long-range effort, but the Brazilian keeper makes a comfortable save.
Neat turn from Traore but it's straight at Alisson as Wolves struggle to get an equaliser.— Sky Sports Premier League (@SkySportsPL) March 15, 2021
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75th min: Saiss very nearly picks out the substitute Fabio Silva at the back post, but Alexander-Arnold is there to clear the danger as Wolves press for an equaliser.
79th min: Mane picks up the ball and drives at the heart of the Wolves defence before getting a shot away, which is comfortably gathered by Patricio before Alisson saves Silva's header at the other end.
80th min: Mohamed Salah gets a shot away from a tight area which Patricio saves, and the Wolves keeper then prevents Jota from adding to his tally seconds later.
85th min: Morgan Gibbs-White so nearly makes an immediate impact off the bench, but Kabak is there to prevent the Wolves man racing through on goal after Silva's neat flick.
86th min: Salah thinks he has wrapped up the three points for Liverpool as he latches onto Alex Oxlade-Chamberlain's pass before slotting home, but the goal is ruled out for offside.
90th +11 min: Major concern for Patricio after the disallowed goal following a clash with Coady, as the stretcher is brought out onto the field after Wolves have already made their three substitutes. However, John Ruddy will see out the game as a concussion substitute after a long delay in play.
90th +14 min: Salah has another chance from the right-hand side of the area, but his curling effort is wide of the mark.
90th +15 min: Silva once again is presented with the opportunity to beat Alisson with a close-range header, but the ball cannons off his shoulder into the goalkeeper's grateful hands.
MAN OF THE MATCH - DIOGO JOTA
Trent Alexander-Arnold deserves a shoutout, but not only has Diogo Jota just made his return from a serious injury, the Portuguese winger marked his return to the Molineux turf in perfect fashion on Monday night.
Leading the line with Roberto Firmino unavailable, Jota took it upon himself to score the decisive goal and give Liverpool a significant boost before the break, although there were certainly questions over Patricio's goalkeeping at his near post.
As the recovering Raul Jimenez was watching on from the stands, Wolves were forced to witness the harrowing sight of Rui Patricio being stretchered off following a sickening clash with Conor Coady after Mohamed Salah's disallowed goal.
Play was stopped for almost 15 minutes as the Portuguese shot-stopper received medical attention on the field, and one can only wonder what must have been going through Nuno Espirito Santo's mind as his first-choice keeper lay motionless on the grass.
158 - James Milner is making his 158th Premier League appearance as a substitute, the joint-most in the competition's history alongside Peter Crouch. Super.— OptaJoe (@OptaJoe) March 15, 2021
Possession: Wolves 53%-47% Liverpool
Shots: Wolves 10-12 Liverpool
Shots on target: Wolves 5-4 Liverpool
Corners: Wolves 3-2 Liverpool
Fouls: Wolves 17-10 Liverpool
Wolves (3-4-3): Patricio (Ruddy 90'); Boly, Coady, Saiss; Semedo (Gibbs-White 84'), Neves (Dendoncker 76'), Moutinho, Jonny; Traore, Jose (Silva 70'), Neto
Liverpool (4-3-3): Alisson; Alexander-Arnold, Phillips, Kabak, Robertson; Fabinho, Wijnaldum (Milner 67'), Thiago (Keita 67'); Salah, Jota (Oxlade-Chamberlain 81'), Mane