All the goals came in the first half as Liverpool's record signing helped his side close the gap on fifth-placed Tottenham to five points, although Spurs have a game in hand.
City remain three points further up the table in fourth place but they will have much to ponder after a wretched performance during which they lost skipper Carlos Tevez to a hamstring injury early on.
The Argentina striker must now be a major doubt for Saturday's FA Cup semi-final against Manchester United at Wembley.
Carroll struck with a fierce left-foot drive after 13 minutes and a 35th-minute header.
His second goal came almost immediately after Dirk Kuyt's low shot.
Liverpool pushed for a fourth and Pepe Reina had to make a smart stop to deny Yaya Toure from long range but there were no further goals, and the night belonged to Liverpool and the Kop's new Geordie hero.
Signed as the replacement for Fernando Torres, the 22-year-old has got his name on the scoresheet before Chelsea's £50million Spaniard.
In a superb all-round performance, he dominated City defender Vincent Kompany in a manner the Belgian has not experienced all season, lashed home a first in quite brilliant fashion after only 13 minutes and was credited with another when Aleksandar Kolarov's header bounced off the Geordie and into the net.
Between those two, Kuyt also struck, leaving City beaten, bruised and wondering what fate has in store for them against their neighbours in six days' time.
With a favourable run to the end of the season, the Blues must have felt as if a decent result on Merseyside would have allowed them to confidently look ahead to Champions League combat next season.
Not in their worst nightmares could they have imagined what was about to unfold.
With Torres in Manchester ahead of Chelsea's Champions League clash with United at Old Trafford and Edin Dzeko in Roberto Mancini's starting line-up, three players who cost a combined fee of £112million during the January transfer window were within a 35-mile radius.
That they had not scored a combined Premier League goal between them has been a subject of intense debate.
By half-time, Carroll had two.
The first was a beauty.
Luis Suarez had already seen a shot touched onto the post by Joe Hart when Raul Meireles let fly with a long-range shot that crashed into Kompany.
The ball ricocheted straight to Carroll, whose first-time effort was hit with far too much power for Hart to keep it out.
Anfield erupted. Yet it was only the start.
When Kompany got himself in the way of a Fabio Aurelio effort, he could only divert the ball across the area, straight into the path of a gleeful Kuyt, who joyfully sent a precise finish into the bottom corner.
As a shellshocked City struggled to clear their heads, Liverpool struck again.
This time Meireles swept a cross to the far post after young full-back Dedryck Boyata had lost possession deep inside his own half.
Kolarov won the aerial duel with Carroll but it was a measure of City's evening that the Serb merely headed the ball against the man he was marking, from where it looped into the net.
For City boss Roberto Mancini, it must have felt like the sky had fallen in as, just for good measure, it started chucking it down too before half-time.
Yet potentially, the worst moment of all came in the minutes after Carroll's opener when Tevez pulled up with what he indicated was a hamstring injury.
The South American gave the signal for a pull as he made his way off the field. Mario Balotelli was immediately introduced. City's stunned fans could only hope it was a precautionary move. The reality seems certain to be rather more depressing.
Kuyt came agonisingly close to twisting the knife a little bit deeper when he flicked a header narrowly wide of the City goal at the start of the second period.
Given they were in the process of amassing 13 points against the current top four, it did beg the question why have Liverpool been performing quite so badly against the Premier League's lesser lights.
That was a reflective point though.
Mancini is the one who needs to find answers quickly as he enters the most important spell of his short Eastlands tenure.
James Milner, normally one of the most level-headed players, reacted with obvious anger when he was replaced by David Silva with less than an hour gone.
Not that there was any noticeable improvement from the Blues, with Balotelli producing a typically enigmatic display before suffering the ignominy of becoming a substitute who was substituted as Nigel de Jong was introduced.
Yaya Toure brought a decent save out of Reina with a 35-yard thunderbolt.
Fittingly though, Carroll almost had the last word when he looped a header onto the roof of the net before departing to a standing ovation just before the end.