Diogo Jota marked his return to Wolves with a winning goal as Liverpool earned a 1-0 victory at Molineux on Monday.
Making his first appearance at his former home since a £45million transfer last year, the Portuguese netted the decisive strike of a tightly contested game.
That ensured Jurgen Klopp's side built on a recovery started against RB Leipzig in the Champions League to move up to sixth in the Premier League table.
The hosts, meanwhile, continued an up-and-down campaign with a 12th league defeat that was further soured by the late loss of goalkeeper Rui Patricio to a head injury, which prompted a 14-minute stoppage and the use of a concussion substitution.
A quick start from Wolves resulted in a strong penalty claim inside the first three minutes, Alisson perhaps fortunate not to be punished for bringing down Nelson Semedo after spilling an Adama Traore cross.
But after the hosts wasted a number of promising counter-attacking opportunities, Liverpool began to grow in confidence and should have been ahead when Sadio Mane was played through on goal but failed to sort his feet in time to shoot.
The game continued in back-and-forth fashion thereafter, with Ruben Neves wasting Wolves' best chance when he drove well wide following a cross to the back post that gave him plenty of time.
And that miss was punished seconds before the half-time whistle as the returning Jota finished off a sweeping move involving Mane and Mohamed Salah with his left foot.
Nuno Espirito Santo's men started the second half as brightly as they had the first and would have hoped to see Conor Coady do better than head over an inviting cross after a half-cleared corner.
They continued to pile pressure on the champions, though, with only a strong hand from Alisson preventing a low Traore cross from being turned goalward.
Wolves struggled to create anything more meaningful across the remainder of the match, however, and could have been beaten more comfortably had a tight offside call not denied Salah four minutes from the end of normal time in an incident that saw Patricio sustain a concerning blow.