Diogo Jota rekindled Liverpool's Premier League top-four hopes with the winning goal on his return to Molineux in a game that ended with a worrying head injury to Wolves goalkeeper Rui Patricio.
Jota, who joined Liverpool from Wolves in September, drilled a low first-time shot under Patricio to settle a tight contest.
It was a fine way for the Portugal forward to mark his first appearance back at his former employers and it sees the Reds climb to sixth, two points behind West Ham in fifth and five off Chelsea in fourth.
In a game of few clear-cut chances, Mohamed Salah saw a late effort ruled out for offside.
However, more distressing for the hosts was the sight of Patricio leaving the pitch on a stretcher after a lengthy delay following a collision with his captain Conor Coady, while trying to prevent the Egyptian from scoring.
The evening started brightly for Wolves who were hoping to win back-to-back games at Molineux for the first time this season.
And while they generally acquitted themselves well, all thoughts of their performance and the result faded late on with Patricio's injury.
Sat in the stands, Wolves forward Raul Jimenez provided a painful reminder of the dangers that footballers can face, with the Mexico international still to return from the fractured skull he sustained against Arsenal in November.
There was a 15-minute delay until John Ruddy was brought on as a concussion substitute to replace the Portugal goalkeeper.
The referee's assistant did not raise his flag for offside immediately, as is the guidance when the video assistant referee is in use, although it is unclear if an earlier decision would have averted the collision because of the speed at which it unfolded.
While the scenes on the pitch had echoes of Jimenez's injury, thankfully Wolves boss Nuno Espirito Santo was able allay fears over the health of his goalkeeper in his post-match interviews.
"Rui Patricio is OK. He's conscious, he's aware," said Nuno. "He remembers what happened. The assessment is positive, he is going to be OK.
"When it's something so serious, you always get worried. It can happen in football. The law is clear. The referees keep the flag down and play to the whistle. Situations will happen. This won't be the only time."
The champions arrived at Molineux after an alarming run of six defeats in their past seven Premier League games.
But this result shows they cannot be discounted from being involved in the final reckoning when it comes to the Champions League places.
As the first half developed so too did Liverpool's confidence.
And there were plenty of flickers of quality from the Reds, who so resoundingly won the reverse fixture 4-0 at Anfield in December.
Many of their best moments arrived courtesy of Sadio Mane's intelligent movement, with the Senegal forward having three good opportunities to score before teeing up Jota's opener.
That gave Jurgen Klopp's side a welcome half-time lead for the first time in nine top-flight matches.
Yet while it was an improvement there were also plenty of signs that more must follow.
Fabinho and Thiago Alcantara's partnership in midfield is a work in progress and despite all their neat interchanges there are still problems in attack which need to be resolved over the remaining weeks of the season.
That was underlined by Jota, Salah, Ozan Kabak and Mane all failing to add to their tally when presented with reasonable opportunities to make life more comfortable for the Reds.
"It's all about the result," Klopp told Sky Sports. "A big fight. If we want three dirty points, I'm fine with that. We had very good moments where we should have done better. Defensively the whole game was really good."
Wolves manager Nuno Espirito Santo told BBC Sport: "It was a very competitive game. We were able to control most of Liverpool's situations.
"There are positives and things we have to improve - better passing and finishing. We must be accurate in the final touch. We know the players can do much better."
On when Raul Jimenez may return: "We don't have a date. We cannot rush things. He's training, not too involved - he must avoid contact. He will join Mexico [to train]. Hopefully we'll still have him this season but we have to be patient."
Liverpool manager Jurgen Klopp told BBC Sport: "It's unfortunate [on Patricio's injury]. In contact sport it happens time to time. I'm more relaxed because the first impression is it's not serious. We wish him all the best. It should not happen, but it can happen.
"We had good moments but the final touch, final pass was not exactly there. We wanted the result."
Source: BBC