Liverpool maintained their undefeated Premier League record on Thursday after a slim 2-1 victory at Molineux Stadium.
Jordan Henderson headed home Trent Alexander-Arnold's eighth-minute corner to make it 1-0, but the Reds lost Sadio Mane to injury before half-time.
Wolves equalised six minutes into the second half when Raul Jimenez nodded Adama Traore's cross past Alisson Becker after a devastating counter-attack.
The hosts dominated for long spells in the second half, but a sucker-punch from Roberto Firmino wrapped up the win with six minutes remaining.
Jurgen Klopp's men got off to the perfect start as they immediately found their rhythm at the Molineux Stadium.
Alexander-Arnold was once again a creator for the European champions, and his dangerous corner nullified Wolves' defence.
Mane jumped for the ball but missed, allowing Henderson to power a header beyond the diving Rui Patricio.
The hosts had an immediate chance of an equaliser, but Matt Doherty agonisingly watched his header go wide.
Doherty beat the offside trap from a set piece, finding himself unmarked at the back post. However, the Republic of Ireland international failed to test Alisson when he should have hit the target.
The full-back's chance was the best opportunity of the first half, and both teams struggled to impose themselves in attack.
Mane's night quickly drew to an end after receiving a knock on 33 minutes. The forward was replaced by recent signing Takumi Minamino.
James Pearce of the Athletic called the action during the interval:
James Pearce @JamesPearceLFC
HT: Wolves 0 #LFC 1: Henderson's early header putting the PL leaders in the driving seat at Molineux. Chances thin on the ground since the opener. Wolves having their moments but the Reds' backline holding firm with Van Dijk immense. The loss of Mane to injury a real blow.
Liverpool nearly doubled their advantage at the start of the second half when Mohamed Salah dispossessed Traore on the edge of his own box. The Egyptian fired a powerful shot which was turned away by Patricio.
However, Traore quickly atoned for his mistake as he made a vital contribution at the other end of the field. A swift counter allowed the hosts to equalise, as the winger perfectly found Jimenez free in the box.
Liverpool's defence failed to deal with Traore's threat, and Andrew Robertson was soon in the book for a foul on the marauding Spaniard.
The Reds didn't find a groove after conceding, and they were second-best in multiple battles across the pitch.
However, it was Salah who should have made it 2-1 with 20 minutes remaining and the striker smashed his effort inches wide.
Wolves continued to apply extreme pressure on Liverpool, but the league leaders found a way to win, just as they have all season long.
A late attack saw Salah and Henderson cause havoc on the edge of the Wolves box, and Firmino manufactured a chance which he smashed into the back of the net.
It was a cruel end to the night for Nuno Espirito Santo's men, who certainly deserved a share of the points, but Liverpool's ruthless attack was once again the deciding factor in the final moments.
Liverpool are back in action on Sunday when they travel to Shrewsbury in the fourth round of the FA Cup. Wolves next play in the Premier League at Manchester United on February 1.