First-half goals from Sergio Aguero and Yaya Toure were backed up by James Milner's 75th minute penalty which came just minutes after Gareth Barry, in his 450th Premier League appearance, was sent off for a second bookable offence.
The home side looked the more likely to score from the outset although the Reds had 13 attempts on goal although just five of those were on target as Kenny Dalglish and his men remained sixth on the table with their first defeat in six.
City took the lead in rather fortuitous circumstances in the 10th minute when Liverpool lost the ball in midfield with Aguero receiving a pass from David Silva outside the area and sending a curling shot on target which dipped under Pepe Reina in what was a very uncharacteristic error by the normally reliable Spanish keeper.
Just over 20 minutes later, and after a good period of play from the Reds, City went two up thanks to Toure's header from Silva's corner which cannoned onto the underside of the bar from the edge of the six-yard box.
The 73rd minute saw Barry received a second yellow for an innocuous bump on Daniel Agger but as Liverpool looked to take advantage of having an extra man, City broke and were awarded a questionable penalty when Toure stormed into the area and was adjudged to have been brought down by Martin Skrtel.
Milner stepped up to the spot and finished coolly into the right corner with Reina committing the other way to wrap up proceedings as City were led brilliantly by Vincent Kompany who was a tower in defence.
City keeper Joe Hart came up with a brilliant early save in the eighth minute when Stewart Downing was sent through by a inch-perfect ball from Jordan Henderson but the England number one got low to snuff the chance moments before Edin Dzeko forced Reina into a stop from a tight angle.
Kompany's glancing header from a corner in the 32nd minute was superbly kept out by Reina about ten minutes before Kompany made a crucial block to deny Dirk Kuyt from close range.
The second half was lackluster apart from the sending off and the penalty with the best chance coming to City sub Adam Johnson who hit the upright with a shot that skidded off the greasy turf to beat Reina but not the woodwork.
In the end though, Roberto Mancini's men were too powerful for the visiting Reds and got the title challenge right back on track after a mini derail early in the New Year.
TRIBAL ASKS: Is this the type of performance that will give Man City plenty of confidence going into the second half of the season? How does Mancini replace Yaya Toure, who is off to the African Cup, who was brilliant tonight?
Etihad Stadium, Manchester - 47,131
Red card:MANC - Gareth Barry 73'