The No.9 fired in at the second attempt after just six minutes before substitute Dirk Kuyt bundled in a late clincher as Kenny Dalglish's side warmed up for next week's curtain-raiser with Sunderland in style.
The Reds played some vibrant attacking football at times and the added bonus of a clean sheet will have left the squad buoyed heading into 2011-12.
On what began as a sunny afternoon in L4, Fabio Aurelio's first appearance since May was the subject of the pre-match natter as a trio of the club's new recruits were also handed their first Anfield experience in a red shirt.
Stewart Downing, Charlie Adam and Jordan Henderson were all starters as the boss looked to use the encounter as a dress rehearsal for the showdown with the Black Cats.
The visitors arrived in the early stages of their preparations for 2011-12 and the opportunity was there for Liverpool to make a fast start.
An exquisite flick from Alberto Aquilani had the Kop purring early doors before Downing and Henderson combined to tee up an almighty goalmouth melee that Los Che just about survived.
Next it was Aurelio's run and pass that released Downing once again but the winger's teasing, low cross just evaded Carroll in the centre.
There was a definite feeling in the air that Liverpool weren't far off an opener and on six minutes they were handed the initiative.
David Albelda under hit a woeful back pass allowing Carroll to rampage in on goal. The England forward saw his first shot rebound back off the post via Diego Alves's fingertips and had to follow in to tuck home from a tight angle.
It was the perfect start for King Kenny and co but there joy was soured just moments later when Glen Johnson was forced off through injury.
The visitors had barely set foot in the Reds half at the quarter of an hour mark but finally gave a warning of their quality on the break when Mehmet Topal came close to diverting a left-wing cross beyond Pepe Reina.
Liverpool responded and Henderson let fly with a low effort from distance before Carroll once again took advantage of a defensive error, but this time his shot was too tame to beat Alves.
The frustration seemed to get the better of the England man who responded by launching into a late challenge on Adil Rami that may well have resulted in more than a yellow card in a competitive encounter.
Read more: Liverpool FC Official
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Jovanovic, now 30, joined Liverpool on a free transfer from Standard Liege last summer, but he was unable to establish himself in the Premier League.
Liverpool is going to meet Valencia tomorrow. Liverpool v Valencia match will be held at Anfield in a pre-season friendly match. Watch Liverpool v Valencia live stream online with 
Kenny Dalglish is working hard to shipped out the deadwoods at Anfield to refill his transfer kitty for at least one more new player before the new season kick-off.
According from source close to the club, another midfielder, Joe Cole looks set to return to West London to join Queens Park Rangers on loan for the 2011/12 season.
Jovanovic joined Liverpool on a free transfer from Standard Liège last summer, having impressed the then manager Rafael Benítez, but was unable to establish himself in the Premier League and last started a game for Liverpool in January. Anderlecht have not paid a fee for him.
