The Reds sent an early warning shot as Luis Suarez stole possession and fired in a shot that Joe Hart just managed to tip onto his upright.
However, the opening goal of the game arrived on 13 minutes when Raul Meireles’ weak effort was blocked by Vincent Kompany and Carroll reacted by rifling a low left-foot shot past Hart from the edge of the area – his first goal since making the £35m switch from Newcastle United in January.
City’s night worsened moments later when talismanic forward Carlos Tevez was forced off with a hamstring injury, and he now looks set to miss this weekend’s FA Cup semi-final showdown with Manchester United.
Liverpool then put the game to bed with two goals in two minutes as Dirk Kuyt produced a clinical finish on 34 minutes before Carroll beat Alexandar Kolarov to head home a Raul Meireles cross.
Meireles forced a decent stop from Hart as City failed to muster anything of note until the 82nd minute when under-worked Pepe Reina kept out a powerful strike from Yaya Toure.
Moments later Mario Balotelli, who had replaced Tevez in the first half, suffered the embarrassment of being substituted, and City nearly suffered further humiliation in the final moments but Carroll’s header landed on the roof of the net.