Harvey Elliott scored the only goal of the game with a stunning long-range strike as Liverpool lifted the gloom by beating Wolves to reach the FA Cup fourth round.
Elliott was one of eight players to come into the Reds side following a chastening 3-0 Premier League defeat at Brighton and Hove Albion, and the teenager made his mark with a sublime first-half finish.
Wolves felt aggrieved not to have won the third-round tie at Anfield after having what appeared to be a late winner ruled out for offside, but they did not pose a threat in the replay at Molineux on Tuesday.
Victory for Jurgen Klopp's side was their first in four games, setting up an opportunity to exact revenge on Brighton in the fourth round.
Liverpool quickly sparked into life after the floodlights briefly went off in the first minute, and Elliott put them in front with a stunning strike.
The teenage midfielder burst forward on the break and let fly with a left-footed strike from 25 yards that flashed past Jose Sa in the 13th minute.
Kostas Tsimikas fired over the crossbar and Cody Gapko was also off target, before Adama Traore showed a complete lack of composure when he drilled wide from a tight angle in a listless first-half display from Wolves.
Julen Lopetegui made a double substitution at the break, introducing Matheus Nunes and Nelson Semedo, but Wolves continued to look short of ideas going forward.
Mohamed Salah entered the fray with 25 minutes to go in a second half that was devoid of quality, with Wolves captain Ruben Neves sending a free-kick just over the bar from a promising position.
The hosts applied some pressure but were unable to fashion an equaliser as the Reds came out on top in a forgettable all-Premier League encounter.