The England striker, who joined on a 35 million pound transfer in January, smashed a powerful shot on his favoured left foot to make it 1-0 in the 13th minute and hit the third goal with a glancing header in the 35th minute of the Premier League match.
Dirk Kuyt found the net in the 34th in a slick and vibrant display from Liverpool that extended its run against Man City at Anfield to nine straight victories.
Liverpool stayed sixth in the standings but moved within five points of No 5 Tottenham in the sole Europa League qualifying position, albeit having played one more match.
Fourth-placed City has also played one more game than Tottenham and is only three points above Spurs in the final Champions League berth.
Worse still for City, captain Carlos Tevez was replaced early in the match with an apparent hamstring injury only days before the FA Cup semifinal against Manchester United.
Due to a defensive crisis that has claimed Daniel Agger, Glen Johnson, Martin Kelly and Sotirios Kyrgiakos to injury or illness, Liverpool manager Kenny Daglish gave 18-year-old John Flanagan a debut at right back.
With the semifinal in mind, City manager Roberto Mancini made three changes from the team that thrashed Sunderland 5-0 last week.
Striker Edin Dzeko, still to score in eight league matches since joining from Wolfsburg in January, replaced Mario Balotelli, while midfielders Gareth Barry and James Milner also came in for Nigel de Jong and David Silva.
Liverpool started with plenty of verve, passing the ball from wing to wing as Luis Suarez probed for openings just behind Carroll.
Carroll's first goal came after a speculative long-range shot from Raul Meireles was blocked by Vincent Kompany. The ball landed for him to strike a low swerving shot that flew past 'keeper Joe Hart in a goal reminiscent of his first for England last month against Ghana.
Liverpool then scored twice within 93 seconds.
Desperate defensive lunges by City players had blocked goal-bound shots on three occasions before Kuyt collected his ninth league goal of the season, sliding the ball across Hart and inside the far post in the 34th minute.
Almost immediately it was 3-0.
Carroll competed with Aleksandar Kolarov in an aerial battle near the penalty spot and glanced the ball from Meireles' pinpoint cross beyond a diving Hart.
After such a dominant first-half display, Liverpool failed to reach similar heights after the break, with City midfielder Yaya Toure's powerful drive forcing Reds goalkeeper Pepe Reina into making the best save of the second period.
The burgeoning partnership between Liverpool's forwards almost brought Carroll a hat trick, his header from Suarez's chipped pass just looping onto the roof of the net in the 87th minute.
