Carroll converted his first Premier League goal since October 29 early in the second half and then Craig Bellamy and Dirk Kuyt added to Wolves’ misery.
Only a fine display by Wolves keeper Wayne Hennessey prevented the Reds from at least doubling their final tally and the home fans chanted “what a load of rubbish” at the final whistle.
Victory completed a memorable seven days for Liverpool after their Carling Cup and FA Cup triumphs over the two Manchester clubs.
But Wolves have now gone nine league games without a win and collected just four points in that spell to increase the pressure on manager Mick McCarthy.
Liverpool were the first to threaten and almost went ahead after two minutes.
Carroll got a touch onto a cross from Bellamy and flicked it on to Kuyt inside the six yard box.
But his control let him down and his eventual shot hit the outside of a post.
Wolves threatened for the first time when Michael Kightly played in Dave Edwards but he failed to make a full contact on his shot on the turn and Jose Reina was able to save.
Charlie Adam became the first player to be yellow carded after 13 minutes for chopping down Matt Jarvis in full flight.
Hennessey was relieved when Bellamy poked the ball past the post after getting in behind the Wolves defence.
Bellamy looked full of purpose and forced Hennessey to save low to his right with a low, dipping drive.
Hennessey made a fine save to keep out a Daniel Agger header with his right foot from an inswinging Bellamy corner.
Then Adam screwed a shot wide after being allowed to advance unmarked to the edge of the Wolves box.
Bellamy was yellow carded after 27 minutes for slicing down Steven Fletcher on the touchline when in full flight.
Wolves were creating chances of their own and Fletcher was only just too high with a header from a Kightly corner.
Hennessey again distinguished himself with a fine save away to his right to deal with Bellamy’s curling 25 yard free-kick.
Bellamy was a constant threat and was again denied by Hennessey with a low save at his near post.
Wolves retaliated and Kightly was inches wide with a low 20-yard effort after linking up well with Fletcher.
Hennessey showed great awareness in racing 20 yards out of his goal to clear from the feet of Kuyt after he had been found in space by Carroll.
But after 52 minutes Carroll put the Reds in front with his fifth goal of the campaign – and third in the Premier League.
Bellamy’s throw found Adam in space and he had time to send over a cross from the left flank.
Carroll timed his run perfectly to turn it past Hennessey.
Liverpool were now in total command and nine minutes later Bellamy doubled their lead with his ninth goal of the campaign.
He was allowed to run unopposed towards the Wolves box before shooting but Hennessey would have been disappointed not to get a firmer hand on his shot which ended up in the corner of the net.
Wolves were in disarray and Agger headed wide from close range after Martin Skrtel had headed the ball into the danger area.
Agger was yellow carded for a challenge on Fletcher and Edwards was booked for a foul on Glen Johnson.
Liverpool were in complete command and Hennessey tipped over a deflected drive from Kuyt.
But after 78 minutes it came as no surprise when Kuyt made it 3-0 from a narrow angle with Adam the creator.
Carroll looked full of confidence after his goal and headed just wide from a Bellamy corner.
At least Wolves finished brightly and substitute Sylvan Ebanks-Blake crashed a 35-yard drive against the post.