Liverpool 2-1 Wolves
Liverpool resisted a second-half fightback from Wolves to secure a hard-fought victory and end a run of back-to-back Premier League defeats.
Kenny Dalglish's side took the lead when Charlie Adam's shot was headed into his own goal by Roger Johnson.
Jose Enrique's long ball over the top was fired in at close range by Luis Suarez for the Reds' second.
And although Steven Fletcher cut the deficit for Wolves, tucking in Stephen Hunt's cross, the home side held on.
It was a much-needed victory for Liverpool after league defeats by Stoke and Tottenham and leaves the Reds with 10 points from their first six matches.
Captain Steven Gerrard, who had returned to action against Brighton in midweek in the League Cup after six months out with a groin injury, came on again for the final 10 minutes.
Craig Bellamy had impressed in the match at Brighton but he was left out as Liverpool manager Dalglish favoured Andy Carroll up front. Carroll had another fruitless afternoon, but came close with a header that hit a post early in the second half just after Wolves had cut the deficit to 2-1.
Despite starting with a 4-5-1 formation for the first time this season, Wolves - who had lost 3-0 in their last Premier League outing against QPR - started well, with Jamie O'Hara shooting from distance at Jose Reina, who collected safely.
It was Liverpool, though, who snatched the lead in fortuitous style in the 11th minute.
After Martin Kelly's cross was cleared by Johnson, Stewart Downing teed the ball up for Adam and the Scotsman's 25-yard shot was diverted past Wayne Hennessey by the Wolves skipper's header.
Johnson protested as he felt he had been fouled while clearing the initial cross as he tussled with Carroll, but the goal stood.
Soon after, Carroll headed at Hennessey and the impressive Suarez then shot wide before Liverpool further extended their lead.
Enrique's chipped pass over the top was met by a perfectly timed run by Suarez, who twisted and turned to leave Christophe Berra struggling before firing in from eight yards.
Suarez came close again, poking the ball wide of the far post as Liverpool finished the first half strongly.
That prompted Wolves manager Mick McCarthy to make a double substitution at half-time as he switched to a 4-4-2 formation.
McCarthy was rewarded after just four minutes when one of the subs, Fletcher, shot in from eight yards after Hunt's cut-back with Reina and Martin Skrtel getting in each other's way.
Liverpool soon came close with a string of chances. Hennessey was outstanding, first blocking a close-range Suarez effort. Carroll hit the post with a back-post header after a cross from the excellent Downing, who later watched a chance of his own being saved by the Wolves keeper.
The game increasingly opened up and Wolves had opportunities of their own as Jamie O'Hara shot off target and Berra threatened with a header.
Gerrard emerged with 10 minutes to play as he replaced Suarez - who kicked a water bottle in frustration at his withdrawal - and struck over from 30 yards as Liverpool held on.
Liverpool manager Kenny Dalglish: "It's interesting - when big Andy Carroll plays half decent, nobody comes in and asks an Andy Carroll question. [He did] everything except score a goal. We couldn't have got much more out of the big fella and we were delighted with him and for him.
"I think we deserved three points although it was difficult at times. If we'd [converted all our chances] there'd have been no one left in the stadium with 20 minutes to go. We maybe got a bit of good fortune with the first goal but we deserved a bit of luck. We've not had too much recently."
Wolves manager Mick McCarthy: "We had a difficult first half and an excellent second half. I thought first 10 minutes we started okay but then we conceded a goal, for which I thought Johnson was fouled by Carroll and I was annoyed about that.
"The second one, we tried to play offside and did it badly and it cost us. My goalkeeper is excellent and he has had a good performance but we were a far better team in the second half and that is the level of performance I would expect from us."