Mohamed Salah put the hosts ahead when he pounced on poor defending from Conor Coady to rifle the ball past Rui Patricio at the midway point of the first half, before Georginio Wijnaldum put Jurgen Klopp's side firmly in control in the 58th minute when he curled home a gorgeous effort from the edge of the box. Joel Matip made the points safe in the 67th minute with a powerful header from Salah's cross, with an unfortunate Nelson Semedo own goal completing the scoring 11 minutes later.
The makeshift Liverpool defence had a largely comfortable afternoon, which should stand them in good stead for a December that is littered with winnable fixtures, while a second clean sheet in five days for rookie keeper Caoimhin Kelleher is the cherry on top of a great week for the Reds.
Even the nit-pickiest player rater will struggle to find any blemishes in what was an excellent, professional display from the Premier League champions.
Manager rating out of 10
7 -- This threadbare Liverpool squad is being guided through a hectic period in excellent fashion by Klopp, who has now led his side to a seven-game unbeaten run in the Premier League.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Caoimhin Kelleher, 7 -- A good save denied Daniel Podence a lovely chipped finish in the first half as the young Irishman put in a solid display on his Premier League debut.
DF Neco Williams, 6 -- Booked in the opening few minutes for a cynical shirt pull, but grew into the game and was an ever-present in the final third as he looked to provide an outlet on the Liverpool right. Replaced by Trent Alexander-Arnold after Liverpool's third goal.
DF Joel Matip, 7 -- A calm, assured display from the most senior defender in the home defence and deserved his goal when he stayed forward and buried home a thumping header.
DF Fabinho, 6 -- The Brazilian stand-in centre-back had a difficult moment against Adama Traore in the first half, but was otherwise untroubled on what was a thoroughly comfortable evening.
DF Andy Robertson, 7 -- A beautiful pass through the lines released Mane midway through the first half in what was an excellent night's work from the buccaneering Scottish international.
MF Curtis Jones, 6 -- Always positive and looking to keep the tempo up in midfield. Played his part in Liverpool's fourth when he released Alexander-Arnold into space ahead of his pinpoint cross.
MF Jordan Henderson, 7 -- As steady, reliable and authoritative as we've come to expect from the England man, who never looked rushed or harried by the visitors. Started the move for Liverpool's second with a probing ball over the top and earned a brief rest with the game won, replaced by Naby Keita in the 80th minute.
MF Georginio Wijnaldum, 7 -- Provided some excellent combination play with his midfield and forward colleagues as the Dutchman helped open up the Wolves backline on more than one occasion, capping his display with a delightful finish from the edge of the area early in the second half.
FW Mohamed Salah, 7 -- Pounced on some ponderous defending from Coady to nip in and drill the ball home to put the hosts ahead in the 24th minute, before a superb cross provided Matip with a simple header for 3-0.
FW Roberto Firmino, 7 -- Dipped into his own half to pick up possession during a frustrating opening quarter of the game, but showed his class with some silky touches. Replaced for the final 17 minutes by Diogo Jota.
FW Sadio Mane, 6 -- An eventful game for the Senegalese international, who was given a reprieve by VAR when he appeared to trip Coady, before putting just enough pressure on Semedo for the Wolves man to turn the ball into his own net for 4-0.
DF Trent Alexander-Arnold, 6 (on for Williams, 68) -- Played a major part in his side's fourth with a wicked ball across the Wolves penalty area.
FW Diogo Jota, N/R (on for Firmino, 73) -- A quiet cameo from the former Wolves man.
MF Naby Keita, N/R (on for Henderson, 81) -- Kept the Liverpool midfield ticking over in the final ten minutes.