Andy Carroll had a great opportunity to give the visitors an early lead, but his effort was smothered by Joe Hart.
The City keeper pulled off another save minutes later when he pushed Steven Gerrard's curled shot around the post as Liverpool enjoyed the early possession.
Hart was called into action soon after as he tipped Stewart Downing's volley away when he appeared to be unsighted until the last moment.
The Reds made the breakthrough in the 11th minute after Gerrard slotted in from the penalty spot following Stefan Savic's foul on Daniel Agger.
Carroll headed wide with 30 minutes played before James Milner blasted over from 12 yards.
In an out-of-sorts opening 45 minutes for the hosts, Adam Johnson fired his free kick over the bar with the last action of the half.
City almost drew level early in the second half when Sergio Aguero latched on to Stephen Kelly's backpass. However, the Argentine could only blaze over after Pepe Reina had reduced the angle.
Reina pulled off an instinctive save just before the hour when he pushed away Micah Richards's close-range header from substitute Samir Nasri's corner.
The Spaniard was on hand again five minutes later to save Aguero's tame shot before James Milner dragged his shot wide from the edge of the area.
Aguero nearly found an equaliser in injury time, but his header from Nasri's cross went inches over.