Carroll was in a heap when the final whistle went but the skipper raced over to pull him to his feet.
It was a nice gesture and the Kop responded with a warm ovation for Carroll’s display. This was a step forward for the 6ft 3ins frontman and an afternoon to build on.
Liverpool should have won at a canter but their profligacy in front of goal coupled with Wolves’ gutsy fightback ensured there was a nervy finale at Anfield.
After back to back league defeats, victory was vital but they will need to sharpen up at both ends with games against Everton and Manchester United next up.
At least the Reds will travel to Goodison safe in the knowledge that Suarez is at the peak of his powers.
The Copa America winner was operating on a different level to anyone else on Saturday. He tormented Mick McCarthy’s men and scored his fourth goal of the season with breathtaking ease.
After racing on to Jose Enrique’s perfectly weighted pass, Suarez turned Christophe Berra one way and then the other before lashing the ball inside Wayne Hennessey’s near post.
One back heel close to the touchline left Roger Johnson flummoxed and the Anfield Road End purring with appreciation.
Only the brilliance of Hennessey denied him greater reward for another man of the match display.
Suarez’s goal made it 2-0 seven minutes before the break and at that point Liverpool were threatening to run riot.
They had built on the moment of good fortune early on when Charlie Adam’s wayward 25-yarder was headed into his own net by Johnson.
The defender complained he had been shoved by Carroll in the build up but after some of the decisions Liverpool have had to endure so far this term sympathy was in short supply.
With Lucas Leiva shining in the centre, Stewart Downing flying down the left and Wolves’ lone frontman Kevin Doyle well shackled by Jamie Carragher, the Reds were in complete control.
Carroll nodded too close to Hennessey and then produced a tantalising cross which Suarez narrowly failed to convert.
The second goal finally gave Liverpool breathing space but four minutes into the second half their grip on the game loosened.
Martin Skrtel allowed boyhood Reds fan Steven Fletcher to get away from him in the box and the substitute clinically converted Stephen Hunt’s cross.
The fact that new faces are bedding in – coupled with a few injury setbacks – goes some way to explaining why only one clean sheet has been kept in eight games so far this season.
But there is certainly work to be done at Melwood to ensure that Pepe Reina is given greater protection.
The keeper vociferously voiced his displeasure on Saturday in the direction of a back line he clearly felt were dropping too deep.
Spurred on by their goal, Wolves grew in confidence and as they threw caution to the wind they left gaps for the Reds to exploit.
Hennessey somehow denied Suarez before Carroll rattled the post with a header. Downing should have opened his Liverpool account after racing clear but fired too close to the keeper.
Those misses served to crank up the anxiety levels around Anfield and there was relief when Berra nodded wide.
With the points still up for grabs there was no hiding Suarez’s displeasure at being asked to make way.
A few shakes of the head as he trotted off was followed by him taking out his frustration on a water bottle. He’s a fierce competitor and wanted to see the job through.
In his place Gerrard steadied the ship with a slick cameo which almost brought a dream strike in front of the Kop. It was the first time the skipper had graced Anfield for six months and he got a rapturous reception.
With Gerrard back, Suarez flying and Carroll progressing, there is plenty to be positive about. But as a unit Liverpool will need to raise the bar if they are going to build on this narrow triumph. Tougher tests lie ahead.
LIVERPOOL (4-4-2): Reina, Kelly, Carragher, Skrtel, Enrique, Henderson (Kuyt 72), Lucas, Adam, Downing, Carroll, Suarez (Gerrard 81). Not used: Doni, Coates, Spearing, Flanagan, Bellamy.
WOLVES (4-5-1): Hennessey, Stearman (Doherty 46), Johnson, Berra, Ward, Hunt (Guedioura 81), Henry, Edwards (Fletcher 46), O'Hara, Jarvis, Doyle. Not used: De Vries, Elokobi, Hammill, Milijas.
GOALS: Johnson (og) 11, Suarez 39, Fletcher 49.
CARDS: Kelly, Carroll (Liverpool); Ward, Henry, Hunt, O'Hara (Wolves).
REFEREE: Kevin Friend.
ATTENDANCE: 44,922.