Another for Steven Gerrard on only his second appearance after two months out with an ankle infection ensured the Reds' struggles at home were banished.
Kenny Dalglish's side had drawn four of the last five at Anfield, where they have dropped 12 points so far this season, and for an hour it appeared that run would continue.
However, former Newcastle forward Bellamy - who had scored in the first half to cancel out Daniel Agger's own goal - curled home a free-kick and Gerrard made sure of victory with an angled shot.
It was the first time Liverpool had scored three goals in a match since the August 27 win over Bolton.
The night was supposed to be all about Carroll, who was given the role of main striker in the absence of the suspended Luis Suarez, but the big centre-forward again came up short.
Playing as a lone front man he struggled for support, especially in the first half, and was often found out of position as he chased the ball.
His best chance came in the latter stages of the match when he crashed a header against the crossbar from close range.
But, fortunately for Carroll, Bellamy's eye for goal was a lot sharper to ensure Liverpool - undoubtedly helped by a 31-minute cameo from Gerrard - came from behind to win a match which looked like a struggle at times.
The story of Liverpool's six home draws this season has been one of failing to take chances and the first one created in the 15th minute was a typical example.
Former Magpies left-back Jose Enrique drilled a cross through the six-yard area but Stewart Downing was moving away from goal rather than towards it and the ball rolled to safety.
Charlie Adam fired a 35-yard shot over while Downing drew Tim Krul into a save low at his left-hand post.
Newcastle took the lead in odd circumstances in the 25th minute.
Haris Vuckic was walking towards the bench having been hit in the face by Glen Johnson's clearance but Newcastle played on and when Ryan Taylor swung in a cross from the left the ball just missed Yohan Cabaye only for Agger to inadvertently divert it past Jose Reina under pressure from Demba Ba.
However, within four minutes Liverpool were level through Bellamy.
Cheick Tiote made a poor attempt at clearing Adam's cut-back from the right of the penalty area and Bellamy drive through a crowd of players from 16 yards.
The home side picked up the tempo and Downing's volley was blocked by Jonas Gutierrez while Martin Skrtel flashed a header just wide of the far post from Bellamy's corner.
Early in the second half Cabaye was lucky to escape punishment after catching Jay Spearing halfway up his shin with a late tackle.
Gerrard replaced Adam just before the hour and the captain's first involvement was to whip in a near-post cross which almost picked out Carroll.
When the England midfielder did find the unmarked striker in five yards of space in the penalty area the £35million signing's first touch let him down badly.
Carroll played a decoy role in Liverpool's second goal but the decisive move came from Danny Simpson.
As Bellamy lined up a 67th-minute free-kick the Newcastle defender decided to back-track to the goalline, allowing Carroll to advance towards Krul. When the set-piece came in Simpson got in the way of his goalkeeper and the ball crept between the two of them.
However, Newcastle would have equalised three minutes later when Ba clipped a narrow-angle shot over Reina - only for Skrtel to clear just inches from the goalline.
Despite Carroll's best efforts he seemed destined not to score when his header rebounded off the crossbar.
Bellamy departed, with blood pouring from a cut above his left eye after a clash with Fabricio Coloccini, to be replaced by Dirk Kuyt for the final 16 minutes.
Not to be outdone Gerrard popped up with a trademark third goal in the 77th minute when he ran from deep to collect Henderson's through-ball and side-foot an angled shot past Krul from the left of the penalty area.
It capped an improved second-half performance and helped ease some of the frustration which had been building up at Anfield.
After their bright start Newcastle have now won one in eight and manager Alan Pardew needs to arrest the slide.