Carroll, who was let go by former Anfield boss Brendan Rodgers after just 18 months on Merseyside, scored with a trademark header to sink his old club.
West Ham were already leading through Michail Antonio's early goal when, nine minutes after half-time, Mark Noble floated in a cross and Carroll powered the ball home.
The goal clearly meant a lot to the striker as he celebrated wildly, with the Hammers registering back-to-back wins while ending Liverpool's run of two straight victories.
Liverpool were hugely disappointing and, with just one shot on target all game, rarely looked capable of getting back into the match after Antonio fired the hosts ahead.
Antonio's first goal for the club, against Southampton last Monday, had more than a touch of fortune about it after a clearance hit him on the head and flew into the net.
But there was no doubt about his second of the season as the winger thumped in a close-range header from Enner Valencia's cross after 10 minutes.
Manuel Lanzini, back in the West Ham side after a spell out injured, showed what they have been missing recently with a vicious, swerving shot which crashed back off the inside of Simon Mignolet's post.
Unfortunately the Argentinian midfielder, who had been the game's most influential player, limped off just before half-time with what looked like a recurrence of his thigh injury.
West Ham continued to cause Liverpool problems, though, with Aaron Cresswell's deflected shot forcing Mignolet to save at his near post.
Liverpool, by contrast, were dismal in attack in the first half, and yet they were inches away from going in level at half-time after Emre Can's curler from the edge of the area clipped the crossbar.
The visitors emerged for the second half early, presumably with a flea in their ear from frustrated boss Jurgen Klopp.
They attacked with more purpose and Philippe Coutinho fizzed a shot over before Alberto Moreno's low cross found Christian Benteke, only for the striker to miss his kick in front of goal.
But just as Liverpool threatened to get back into the game Carroll snatched it away from them, rising above Nathaniel Clyne to powerfully nod Noble's cross past Mignolet and into the back of the net.
Carroll could have piled on the misery with another header from Cresswell's cross but Mignolet made a fine save.
Liverpool almost pulled one back with 10 minutes remaining but Lucas' header was cleared off the line by Mark Noble.
TWEET OF THE MATCH
@karren_brady: "Fantastic win COYI"
WEST HAM
Adrian: 6
Aaron Cresswell: 7
James Collins: 8
Angelo Ogbonna: 7
James Tomkins: 6
Cheikhou Kouyate: 6
Mark Noble: 7
Manuel Lanzini: 7
Enner Valencia: 7
Michail Antonio: 7
Andy Carroll: 7
Subs:
Pedro Obiang: 6
Dimitri Payet: 6
Carl Jenkinson: 6
LIVERPOOL
Simon Mignolet: 6
Alberto Moreno: 6
Dean Lovren: 6
Mamadou Sakho: 6
Nathaniel Clyne: 6
Emre Can: 6
Lucas: 5
Jordan Ibe: 5
Roberto Firmino: 5
Philippe Coutinho: 6
Christian Benteke: 5
Subs
Adam Lallana: 6
Brad Smith: 6
Joe Allen: 6
STAR MAN
James Collins
You could have been forgiven for not realising that Christian Benteke was playing as Welsh centre-half Collins completely marked him out of the game, winning every single header the pair went up for.
MOMENT OF THE MATCH
Andy Carroll's goal clearly meant a lot to the striker after his disappointing spell at Liverpool - and boy did he celebrate it.
VIEW FROM THE BENCH
Liverpool were without Jordan Henderson and they missed his calming influence in midfield as pass after pass went stray
West Ham recalled Carroll and the move paid dividends.
MOAN OF THE MATCH
The first-half injury to West Ham's Manuel Lanzini, who was denied a fabulous goal by the woodwork and had been the outstanding player on the pitch until his early departure.
WHO'S UP NEXT?
West Ham v Wolves (FA Cup, Saturday, January 9)
Stoke v Liverpool (Capital One Cup, Tuesday, January 5)
Liverpool boss Jurgen Klopp said: "It's no day for being disappointed, it's a day for being angry.
"We had the ball and possession and bad luck in a few situations - but that's not what I want to see, to be honest
You have to be there in the decisive moments.
"We have to be better
We could have come back but we didn't
Who wants to see 90 per cent? You can't win a game with 90 per cent.
"You need more will than we did today
Two-nil - it's deserved."
West Ham boss Slaven Bilic added on BT Sport: "It's a great win - I think we deserved it.
"We defended well because you have to
We had many opportunities, scored a couple of great goals - and kept a clean sheet.
"We are going to have our ups and downs but we are definitely a good team."
James Collins, who impressed in central defence for West Ham, said: "We had a couple of dodgy results at home earlier in the season but since then we have been solid and not conceding many goals."
Asked about the club's prospects of earning a place in European competition next season, the Wales international added: "It's d efinitely moving that way
"We're disappointed how we played in the Europa League earlier in the season - but looking back maybe it was a good thing
We've got high ambitions."
Source : PA
Source: PA