Carroll rose to meet a precise cross from Mark Noble 10 minutes into the second half, doubling the hosts' advantage after Michail Antonio had headed them into an early lead.
West Ham moved up to fifth in the table, two points above Liverpool whose frailties were exposed again at Upton Park.
Having won their last two games by narrow margins, Juergen Klopp's side looked more like the team that took a solitary point from their previous three, with little threat in attack and familiar vulnerabilities in defence.
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Carroll, who remains Liverpool's record signing when he joined the Anfield club for 35 million pounds ($51.6 million) in 2011, almost made it 3-0 when he had another header saved by Liverpool keeper Simon Mignolet.
The visitors, however, were largely restricted to shots from distance and two half-hearted penalty appeals for handball as they tried in vain to reduce the deficit.
Substitute Joe Allen sent a header narrowly wide at the death, a rare clear-cut chance on an otherwise disappointing day for Klopp.
"I'm really angry today because we could have got so much more," the German told the BBC. "Today, we deserved to lose.
"We always had the ball, we could have made much more chances but we didn't. We have to again accept that we didn't play like we should."
Liverpool were unhappy with West Ham's opener as Alberto Moreno appeared to be fouled running down the left flank before the hosts countered with Antonio running the length of the pitch before launching himself at a deep cross to head past Mignolet.
There was an inevitability about the second from the moment Noble shaped to cross the ball with Carroll hovering at the far post.
The England striker rose high above anybody else to direct his header back across goal and into the far corner of the net to ensure West Ham did the double over Liverpool, having won 3-0 at Anfield in August.
"Each game you want to win and score goals, it doesn't matter if it is against a side you have played for," Carroll told BT Sport.
"We don't want to get ahead of ourselves, we just want to keep winning games."
(Reporting by Toby Davis; editing by Ed Osmond)
