Mohammed Salah opened the scoring when he pounced on Conor Coady's error before his low-driven effort found the bottom corner.
Jurgen Klopp's side doubled their lead in the second half when Gini Wijnaldum's long-range effort whistled past Rui Patricio into the top corner.
Joel Matip added the third before a Nelson Semedo own-goal made it four not long after, meaning Liverpool move joint-top with Tottenham Hotspur.
Story of the match
Caoimhin Kelleher remained in goal for his league debut after making his UEFA Champions League debut midweek, and the 22-year-old 'keeper was called into action early on when he denied Wolves' Daniel Podence.
Kelleher managed to scramble across his goal-line to tip the Portuguese's attempted chip wide of the post, much to the pleasure of the 2,000 Liverpool fans in the Kop end.
Liverpool took the lead after 24 minutes through Salah with a little help from ex-red, Coady.
Jordan Henderson's lofted pass looking for the run of the Egyptian was met by Coady, however poor control from the centre-back let the ball fall into the path of Salah who lashed the ball into the bottom right corner.
Wolves were awarded a penalty right before half-time when referee Craig Pawson deemed Sadio Mane's challenge on Coady a foul, however after a check of the pitchside monitor the decision was overturned - with Coady lucky to avoid a booking for simulation.
Liverpool controlled the early stages of the second half, and their second came 60 minutes in through a peach of a finish from Wijnaldum.
Another long-ball from Henderson was brought down by Wjnaldum, and the Dutch midfielder was given acres of space to roam forward on the edge of the box - allowing the 30-year-old to take aim and curl his effort into the top right corner.
The league champions got a deserved third when Matip managed to get his head on the end of Salah's inviting cross and power through Patricio, putting his side out of sight from the visitors.
It was four for Liverpool not long after when Semedo slid the ball into his own net.
Substitute Trent Alexander-Arnold fizzed an outstanding cross into the Wolves box and put it on a plate for Mane, however the Senegalese international's shot was smothered by Semedo - unfortunately into his own net.
Liverpool controlled the ending stages and saw out the rest of the game in comfortable fashion as they moved up to second, going level on points with Spurs.
Reds in safe hands
Liverpool fans would've been forgiven when academy goalkeeper Kelleher was promoted to the first team in the Champions League fixture vs Ajax, but after a strong performance midweek, he more than earned his starting place vs Wolves.
The Irish 'keeper was called into action early on and received loud applause from the fans in the Kop end behind him when he made a brilliant save to deny Podence, and from then on out he oozed confidence - making valuable saves and commanding his area with ease.
A strong performance from the new Liverpool number two.
Leader by example
A big shoutout to Jordan Henderson tonight.
The Liverpool captain was arguably the man-of-the-match tonight, with the 30-year-old controlling the game from midfield, as well as grabbing himself two assists.
He received a much-deserved standing ovation from the fans in attendance, proving once again how vital he is to Klopp's side.