The England striker capped a perfect night for the Reds by scoring only his third league goal of the campaign — the last also came in the Black Country at West Brom in October — and seventh since his £35m move from Newcastle United.
It came just days after speculation had circulated that Carroll could move to Manchester City in a swap for Carlos Tevez.
Manager Kenny Dalglish said: “We do not need to justify the rumours. It was a great goal from Andy. There is no I in team.”
Dirk Kuyt and Craig Bellamy scored the other goals for Liverpool and Dalglish picked out the in-form Welshman, who has now netted six in his last 10 matches.
“The wee man has been fantastic for us,” I wish his numbers were the other way around and he was 23 rather than 32. When he gets it you know something is going to happen.”
It was, however, a miserable night for Wolves, who were jeered by their supporters and are now 11 matches without a win in all competitions and remain rooted in the bottom three — leaving Mick McCarthy under increasing pressure.
The manager said: “After the first half I did not see the second half coming. Watching that second half was unacceptable for me or anybody else. The lads are hurting. They have all gone out their and tried.
“We have been beaten by a considerably better side who have just beaten Manchester City and Manchester United, but of course I understand their reaction.”
Dirk Kuyt should have picked up where he left off against Manchester United on Sunday within four minutes. Bellamy’s inviting left-wing cross was flicked on by Carroll towards the Dutchman, lurking inside the six-yard box, but his first touch was laboured and despite eventually firing into the net, it did not stand as the ball had already squirted out of play.
Wolves sprung into action shortly before the break when Michael Kightly and Steven Fletcher played a neat one-two before the winger unleashed a stinging low shot from the edge of the box which veered just past the post.
The significance of the near soon became evident. Bellamy’s throw-in found Adam and his pinpoint delivery was converted by Carroll at the back post, the striker steering a shot low into the left corner.
Nine minutes later it was two. Jay Spearing, the midfielder, fed Bellamy and, in the absence of enforcer Karl Henry, Wolves allowed Bellamy the freedom to stride towards the edge of the area and pick his spot inside the right corner.
Liverpool were rampant. Kuyt wrapped up the points when he took advantage of more slack defending in the 78th minute, playing a one-two with Adam before slotting home.
Wolves knew their luck was out when substitute Sylvan Ebanks-Blake’s thunderbolt cannoned off a post.
WOLVES (4-5-1): Hennessey 5; Foley 5, Johnson 4, Berra 5, Ward 5; Kightly 6(Hunt 62, 5), Jonsson 4 (Ebanks-Blake 62, 5), Frimpong 6 (Milijas 84), Edwards 5, Jarvis 5; Fletcher 5.
LIVERPOOL (4-2-3-1): Reina 7; Johnson 6, Skrtel 6, Agger 7, (Carragher 81), Enrique 7; Spearing 7, Adam 7 (Shelvey 81); Kuyt 7 (Aurelio 90), Henderson 7, Bellamy 9; Carroll 7
Referee: A Taylor (Cheshire)