The Â£35million winter signing was irrepressible for the Reds, opening his account for the Merseyside club with a thunderous strike in the 13th minute before grabbing his second with a superb header in the 35th, not long after Dirk Kuyt had added the sideâ€™s second.
There were no goals in the second half but that did not stop Liverpool extending their unbeaten league run at Anfield to seven matches and reversing the earlier result of 3-0 at Eastlands in August.
The win kept Kenny Dalglishâ€™s men in sixth place, now five points behind Tottenham in fifth, whilst Roberto Manciniâ€™s charges stretched their winless run away from home to six and have saluted just once against the Reds in 14 Premier League meetings at Anfield to stay fourth.
Venue: Anfield, Liverpool
Referee: Mark Halsey
Yellow cards: LIV - Fabio Aurelio 27â€™
MANC - nil
The Reds had the best early chance when recruits Andy Carroll and Luis Suarez linked up with the ball being played through by Carroll who had opened up the Man City defence for his Uruguayan partner. Suarez was clear through on goal and his poked shot looked like it was destined for the back of the net only for Joe Hart to intervene by getting a slight left hand on the ball to deflect it onto the upright.
It was an exhilarating start from both sides with Liverpool looking in a very positive frame of mind and it paid off when Carroll delivered an absolute cracker in the 13th minute to open up his Liverpool account.
GOAL Raul Meirelesâ€™ slightly mishit shot from way outside the box bounced back off the City defence only to fall for Carroll who whistled it past Hart with his trusty left foot from about 25 yards to get things started for the evening.
Straight after the goal, City skipper Carlos Tevez had to be subbed off with what appeared to be a hamstring injury which will surely have him in doubt for Saturdayâ€™s FA Cup semi-final with Manchester United in what was a major blow for the visitors.
Despite Tevezâ€™s departure, the game continued on with a fairly hectic pace with the home side enjoying the better of the chances before City worked their way forward with more regularity and went close through Edin Dzeko and Aleksandar Kolarov midway through the half.
GOAL After that, the Reds took it straight down the other end and peppered Hartâ€™s goal before it feel to Dirk Kuyt on the right side of the penalty box and he side-footed it with precision from inside the area for his ninth league goal of the season to make it 2-0.
GOAL Less than two minutes later, Liverpool were three ahead when Meireles found space down the left before supplying a pin point aerial pass for Carroll who finished with quite a brilliant header from 12 yards under extreme duress from Kolarov to grab his second, tearing the heart out of the City side.
Anfield was absolutely buzzing after the third but they had to deal with an unwanted half-time break before seeing their heroes back in action on a wet night on Merseyside.
Thankfully from their point of view, the Liverpool players picked up where they left off and came very close in the 51st minute when Kuytâ€™s glancing header from close range missed the target.
Man City were fairly toothless throughout so Roberto Mancini opted to bring on the creative David Silva on the hour mark but it was Liverpool who kept pushing forward with Meireles forcing a top save out of Hart in the 65th minute.
There was no way back for City as the home side went about their business with a few half-chances to Kuyt and Suarez before the Dutchman shot just across the face of goal with ten minutes left.
Meireles had his 82nd minute shot from inside the area well-held by Hart just a moment before Yaya Toure hit an extreme long range shot which required a reaction save from Pepe Reina.
Carroll wasnâ€™t too far away from a hat-trick when Suarez found him at the back post with a deft little chip but the three first-half goals ended up being enough as the Reds recorded a comfortable win with debutant John Flanagan producing a solid first-up performance for his hometown club.
Joe Hart (gk) â€“ Dedryck Boyata, Vincent Kompany, Joleon Lescott, Aleksandar Kolarov â€“ Adam Johnson, Yaya Toure, Carlos Tevez (Balotelli 16 â€“ de Jong 83â€™), Gareth Barry, James Milner (Silva 59â€™) â€“ Edin Dzeko