The Reds had suffered a late Premier League defeat to the same side at Molineux on Tuesday but responded strongly by securing a comprehensive victory to reach the last eight.
After a quiet first half in which Liverpool struggled to create chances or find rhythm, the visitors struck twice within 10 minutes of the restart to take control of the match.
Andy Robertson opened the scoring when he collected a pass from Curtis Jones and drove a 25-yard shot into the bottom corner - his first goal since September. Mohamed Salah doubled the lead just 95 seconds later.
Robertson, who has started only five league games this season and was close to joining Tottenham in January, showed his value again moments later when he delivered the cross that led to Salah’s goal, which was confirmed after a VAR check for offside.
Jones added a third with 16 minutes remaining, curling a shot in from the edge of the area. Wolves grabbed a late consolation in stoppage time through Hwang Hee-chan.
The defending Premier League champions are currently sixth in the table, with the FA Cup and Champions League their remaining chances to win a trophy this season.
Liverpool manager Arne Slot praised his team’s reaction after the defeat earlier in the week.
"The response was perfect," Slot said.
"A lot of ball possession, them creating one chance and scoring one goal that was similar to three days ago. We created more than we did in the last game and that is the reason we could win it today. Almost all things were the same from three days ago except we scored more. Very frustrating to see we have hardly given away any chances, but we still concede a goal."
Slot admitted the victory brought relief in what he described as a "rollercoaster season."
"Every three days I have a different feeling," he said. "Three days ago my feeling was completely different to now. Good to be in the quarter-finals of the FA Cup."
Liverpool next face Galatasaray away in the Champions League round of 16 on Tuesday.
Chelsea fended off a strong challenge from Wrexham to beat them 4-2 after extra time in the FA Cup fifth round on Saturday, keeping their hopes in the competition alive after a dramatic encounter.
Arsenal survived a determined challenge from Mansfield Town as Eberechi Eze struck the decisive goal in a tense 2-1 victory to send the Gunners into the quarter-finals of the FA Cup on Saturday.
Liam Rosenior has hinted that Chelsea's next generation could get a chance to shine when the Blues face Wrexham in the FA Cup on Saturday, with the head coach naming two academy prospects who travelled with the squad.
Eddie Howe has insisted Newcastle United will attack the FA Cup with full commitment as they prepare for another demanding clash with Manchester City this weekend.
