Carroll has struggled to live up to his £35 million price tag since his move from Newcastle and there has been speculation about him being surplus to requirements.
But he looked sharp against Mick McCarthy's side and netted his first league goal for three months, although Liverpool's star performer was Craig Bellamy.
Midfielder Spearing said: "From the moment he signed for Liverpool we've seen Andy's quality.
"It was only a matter of time before it came out on the pitch and against Wolves he showed exactly what he is capable of doing for this club.
"Hopefully he can carry on and keep doing that until the end of the season.
"Andy can cause all sorts of problems in the air, but he's also great with his feet, as you've seen with some of the turns he does and his finish for that goal."
Spearing praised Kenny Dalglish's side for building on their Carling Cup and FA Cup triumphs against Manchester City and Manchester United respectively.
Victory at Molineux lifted them into fifth spot in the Barclays Premier League and kept alive their hopes of securing a Champions League spot.
Spearing said: "After the week we had we knew we had to come to Wolves and do exactly the same.
"Playing Manchester City and Manchester United and coming out with two brilliant results, which were thoroughly deserved, gave us all a massive confidence boost
"But we came to Molineux, didn't take our foot off the gas and proved what we are all about. We've got to take each game as it comes and aim towards that top four.
"We couldn't see Wolves as anything different. It was a Premier League game and we wanted to get three points.
"Right from the off we showed what we were capable of doing and caused them a lot of problems. In the second half we caused them more problems and got the three goals.
"The results we've had have brought the team closer together. We've always been a close-knit group and are starting to show that on the pitch. It was just going to take some time before it started showing."