Harvey Elliott's long-range effort was his fourth goal of the season in all competitions.Liverpool claimed their first win since the turn of the year as Harvey Elliott's stunning strike proved enough to beat Wolves in their FA Cup third-round replay.
Elliott's powerful long-range drive broke the deadlock with 13 minutes on the clock.
Fabio Carvalho had a goal ruled out before Ruben Neves sent a free-kick narrowly off target in the second half.
Liverpool will travel to Brighton in the fourth round on Sunday, 29 January.
Reds manager Jurgen Klopp, who made eight changes to the team beaten by the Seagulls in the Premier League on Saturday, will be thrilled with his side's response to that humbling defeat on the south coast.
Wolves' improvement under Julen Lopetegui has been clear to see but the home side failed to seriously threaten Caoimhin Kelleher's goal until the latter stages of the contest, when Neves, Raul Jimenez and Matheus Cunha all went close to an equaliser.
Reds deliver perfect response
There was a brief stoppage in play within the first minute due to a power cut inside the stadium, but Liverpool's visiting supporters did not have to wait much longer for teenager Elliott to light up Molineux with a goal of the highest quality.
The 19-year-old collected a pass from Thiago Alcantara, advanced unchallenged into the Wolves half and unleashed a ferocious 30-yard effort which sailed over the dive of goalkeeper Jose Sa and into the net.
The goal appeared to settle Liverpool, who continued to attack with pace and intensity while forcing the hosts into errors in possession.
Fabio Carvalho had the ball in the Wolves net again 10 minutes before half-time, but the former Fulham forward was in an offside position from Naby Keita's through-ball and the goal was disallowed.
Wolves' best opportunity of the first half fell to the lively Adama Traore, who raced on to Neves' pass but failed to hit the target from a tight angle.
Lopetegui introduced Matheus Nunes and Nelson Semedo at half-time in an effort to give his team fresh impetus, but the hosts continued to labour in the final third until Cunha and Daniel Podence entered the fray with 25 minutes remaining.
Raul Jimenez and Cunha both failed to hit the target from promising positions, before the latter sent a tame header into Kelleher's arms from an excellent position inside the penalty area.
Fellow second-half substitute Curtis Jones missed an opportunity to double Liverpool's lead when he dragged a shot just past the far post in the 90th minute, but the holders held on for a first clean sheet in eight games and a place in the fourth round.
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Wolverhampton Wanderers
Squad number1Player nameJosé Sá
Squad number81Player nameLembikisa
Squad number4Player nameCollins
Squad number24Player nameToti
Squad number19Player nameJonny
Squad number59Player nameHodge
Squad number8Player nameRúben Neves
Squad number37Player nameTraoré
Squad number28Player nameJoão Moutinho
Squad number3Player nameAït-Nouri
Squad number9Player nameJiménez
Squad number10Player nameDaniel Podence
Squad number12Player nameMatheus Cunha
Squad number22Player nameNélson Semedo
Squad number27Player nameMatheus Nunes
Squad number29Player nameDiego Costa
Line-ups
Wolves
Formation 4-2-3-1
1Sá
81Lembikisa4Collins24Gomes19Castro Otto
59Hodge8Neves
37Traoré28João Moutinho3Aït-Nouri
9Jiménez
1Sá81LembikisaSubstituted forNélson Semedoat 45'minutes4Collins24Gomes19Castro OttoSubstituted forPodenceat 64'minutes59HodgeSubstituted forNunesat 45'minutes8Neves37TraoréBooked at 43mins28João MoutinhoSubstituted forSantos Carneiro Da Cunhaat 65'minutes3Aït-Nouri9JiménezSubstituted forDiego Costaat 84'minutesSubstitutes
10Podence11Hwang Hee-chan12Santos Carneiro Da Cunha13Sarkic22Nélson Semedo23Kilman27Nunes29Diego Costa64BuenoLiverpool
Formation 4-3-3
62Kelleher
7Milner5Konaté2Gomez21Tsimikas
8Keïta43Bajcetic6Thiago Alcántara
19Elliott18Gakpo28Carvalho
62Kelleher7MilnerSubstituted forPhillipsat 66'minutesBooked at 71mins5Konaté2GomezBooked at 90mins21Tsimikas8Keïta43BajceticSubstituted forFabinhoat 75'minutes6Thiago AlcántaraBooked at 57minsSubstituted forDoakat 75'minutes19Elliott18GakpoSubstituted forSalahat 66'minutes28CarvalhoSubstituted forJonesat 66'minutesSubstitutes
1Alisson3Fabinho11Salah15Oxlade-Chamberlain17Jones26Robertson32Matip47Phillips50DoakLive Text
Match ends, Wolverhampton Wanderers 0, Liverpool 1.
Second Half ends, Wolverhampton Wanderers 0, Liverpool 1.
Hand ball by Mohamed Salah (Liverpool).
Attempt blocked. Matheus Cunha (Wolverhampton Wanderers) right footed shot from the centre of the box is blocked.
Corner, Wolverhampton Wanderers. Conceded by Fabinho.
Joe Gomez (Liverpool) is shown the yellow card.
Corner, Wolverhampton Wanderers. Conceded by Ibrahima Konaté.
Attempt saved. Matheus Cunha (Wolverhampton Wanderers) header from the centre of the box is saved in the centre of the goal. Assisted by Matheus Nunes with a cross.
Attempt missed. Curtis Jones (Liverpool) left footed shot from the left side of the box is close, but misses to the right. Assisted by Harvey Elliott.
Matheus Nunes (Wolverhampton Wanderers) wins a free kick in the attacking half.
Foul by Fabinho (Liverpool).
Attempt missed. Matheus Cunha (Wolverhampton Wanderers) right footed shot from the centre of the box is high and wide to the right. Assisted by Diego Costa.
Foul by Matheus Nunes (Wolverhampton Wanderers).
Mohamed Salah (Liverpool) wins a free kick in the defensive half.
Substitution, Wolverhampton Wanderers. Diego Costa replaces Raúl Jiménez.
Attempt blocked. Raúl Jiménez (Wolverhampton Wanderers) header from very close range is blocked. Assisted by Adama Traoré with a cross.
Raúl Jiménez (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Konstantinos Tsimikas (Liverpool).
Corner, Liverpool. Conceded by Toti.
Substitution, Liverpool. Ben Doak replaces Thiago.
