Wolves 0-3 Liverpool
Andy Carroll celebrated the first anniversary of his £35m move to Liverpool by setting the Reds on their way to victory at Molineux.
Carroll, 23, prodded in at the far post at the start of the second half to open the scoring in the Premier League game.
Craig Bellamy added a second with a low finish and Dirk Kuyt scored a third after a quick break.
Victory breathes life into Liverpool's Champions League hopes but Wolves are now without a win in nine games.
It was just Carroll's seventh goal since his move from Newcastle on transfer deadline day last year, with five of that total coming in the Premier League.
He has struggled for fitness and form and has lost his place in Fabio Capello's England squad.
But, with Luis Suarez set to return from his eight-match ban against Tottenham next week, this was an ideal response after Liverpool had to deny reports they had offered him to Manchester City in a potential swap deal for Carlos Tevez.
Carroll won praise for his performance in the 2-1 FA Cup win over Manchester United and once again grew in confidence after giving the Reds, who were without rested captain Steven Gerrarrd, the lead.
The striker only had one half-chance in an open first half and Bellamy posed Liverpool's greatest threat.
The Welshman prodded wide from a fine through ball from Jordan Henderson, had a free-kick held by Wayne Hennessey and was denied on two further occasions by the Wolves goalkeeper.
For the home side, Michael Kightly, having scored his first Premier League goal in the 3-2 defeat by Aston Villa, carried on his good work against Liverpool.
The winger clipped in a great cross that David Edwards prodded straight at Pepe Reina and also took a quick corner that was headed on to the roof of the net by Steven Fletcher.
And Kightly was involved again as he drove just wide of Reina's goal after swapping passes with Fletcher.
At the other end, Hennessey did well to deny Kuyt at the start of the second half, but Liverpool took the lead six minutes after the restart.
Bellamy's quick throw was collected by Charlie Adam, who whipped a cross to the far post for Carroll to beat Eggert Jonsson to touch in at the far post.
Shortly after the hour, as Wolves backed off, Bellamy hit a shot from just outside the area that squirmed past fellow Welshman Hennessey for the striker's sixth goal in seven Premier League starts.
Wolves were reeling and they conceded a third after a Liverpool counter-attack that started on the edge of their own area and ended with Adam rolling a pass to Kuyt, who finished from a narrow angle to score his 50th Premier League goal.
It was the fifth consecutive home game in which 19th-placed Wolves have conceded two or more goals, although Mick McCarthy's side came close to a consolation when substitute Sylvain Ebanks-Blake hit the post from distance.
Wolves were booed off at the final whistle, with one fan unveiling a "Mac Out" banner.
Wolves manager Mick McCarthy:
"We were doing OK, had a corner and didn't mark on the edge of the box and defended poorly for it. That lifted them.
"We've had so many knock-backs that it's bound to be a huge disappointment and the reaction was that. I was trying to get fresh legs on - because of the shape we couldn't get the ball back.
"[The fans' reaction] is fully understood and the last 35 minutes were unacceptable. We were getting a real chasing but they're a great bunch of lads, work their socks off for me and the club, and the shape that I had was making it difficult.
"But I was never going to accept keeping it 4-5-1, defend, and lose 2-0 so I take the blame for the last 35 minutes."
Liverpool manager Kenny Dalglish:
"We had a very thoroughly professional, high-quality performance, and the players deserve great credit after the two victories we've had.
"We thoroughly deserved the victory and the boys were a credit to the club. We're pleased with everybody.
"The first goal was a great ball in from Charlie Adam and a great finish from Andy Carroll who played really well. He's a Liverpool footballer and he will make a contribution for us many times.
"He flicked on one on Saturday for Dirk Kuyt to score against Manchester United and did the same for Craig Bellamy at Bolton. If he gets a goal he gets a goal, but his contribution is fantastic."