Carroll, the most expensive English player after his 35 million pound transfer from Newcastle in January, lashed in the opener from the edge of the box after 13 minutes and added his second shortly after Dirk Kuyt's strike.
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City's first half went from bad to worse after striker and captain Carlos Tevez hobbled off with a hamstring injury and is set to miss the FA Cup semi-final against Manchester United on Saturday.
Kuyt slotted the ball neatly into the net on 34 minutes before Carroll's second, a header from a Raul Meireles cross, left Liverpool in sixth place on 48 points with six games remaining. City remain fourth on 56 points from 32 matches.
"The fans have been fantastic ever since I've been here," a beaming Carroll, who made his debut against United on March 6 after a long spell out with injury, told Sky Sports.
QUALITY SIGNINGS
Fellow forward Kuyt said the signing of Carroll and Uruguay striker Luis Suarez in January had made a huge difference to Liverpool.
"It makes it a lot easier if you get more quality in the team," the Netherlands forward said.
"We were very happy with the signings of Andy and Luis and I think you can already see the quality."
Liverpool will now seek to beat Tottenham to fifth place, and possibly even City to fourth, though Kuyt said the task would be a difficult one.
"We like to look up to fifth place. I know it's very difficult but we have to try," he said.
An apologetic Roberto Mancini said his team would put the defeat out of their minds ahead of the FA Cup derby, Man City's last realistic chance of silverware this season.
"It's important to forget this and we prepare for the semi-final," the Italian said.
"Tonight I made a mistake, it's my fault. I'm very sorry for the fans.
"We conceded a lot of chances in the first 20 minutes, after that we played."
