City dominated the opening period and a Samir Nasri effort meant they deservedly led at the break and their lead was soon doubled when Sergio Aguero headed home just after the interval.
Demba Ba pulled one back just after the hour mark for Chelsea, but City withstood late pressure and held on to book a cup final date with Wigan next month.
The main talking point at the start of the match was Roberto Mancini's decision to start with Costel Pantilimon ahead of Joe Hart - but the Romanian barely had a touch of the ball as City dominated from the first whistle.
Indeed, Petr Cech was needed to keep his side in the match in the opening ten-minutes, saving well from Aguero and then Carlos Tevez.
Just as Chelsea looked to have found a footing in the match, the deadlock was broken by City - although there was some luck about it for Nasri.
Yaya Toure created the chance as his marauding run could not be stopped, he fed Aguero in the box who in-turn played in Nasri - he looked to play it back to the Argentine - but instead it hit Cesar Azpilicueta and cannoned straight back to the Frenchman to side-foot home from six yards.
Moments later and the lead should have been doubled, but this time fortune was on Chelsea's side as the ball dropped for James Milner just inside the box, taking a touch he unleashed his shot - which beat Cech, but hit Aguero - who could do little but block the goal-bound effort.
Yet another chance came City's way on the stroke of half time as they countered brilliantly from a Chelsea free-kick at the other end - the charge was led by Milner and Roberto Mancini's men had five on three - but the England midfielder's cross into the box was poor, but Cech's clearance still fell for the on-rushing Vincent Kompany - who could only volley wide.
City then began the second period as they finished the first, and within two minutes the lead was indeed doubled.
Gareth Barry created the chance with a wonderful ball into the box and Aguero rose superbly to loop his header into the far corner of Cech's goal, leaving the Czech star helpless.
Unsurprisingly, City were happy to counter on Chelsea, who had no option but to push forward and look for an opening and introduced Fernando Torres on the hour, and within minutes they had a goal back.
A long ball from David Luiz was not dealt with by City, and Ba just held off Kompany before helping the ball into the corner of the net with an acrobatic effort.
Suddenly Chelsea were in the cup tie as the momentum had totally changed, and not long after they should have levelled as Eden Hazard led a counter attack, he looked to play in Juan Mata and the Spaniard got the ball as Matija Nastasic failed to deal with the clearance but Pantilimon was off his line brilliantly to slide in and palm it away.
The Romanian then made a top-drawer save to keep Ba out as Hazard escaped the attentions of Kompany in the box - and suddenly City were on the back foot. Luiz stuck a free-kick just wide of the post and he was then on the receiving end of a two-footed lunge from Aguero, who was hugely fortunate not to see red.
Chelsea continued to press and Torres had a couple of half chances, but they could not find a way though as their grasp on the FA Cup was wrestled away from them.