Demba Ba pulled one back for the Blues but they were unable to find an equaliser to send the match into extra time.
Here, Sports Mole casts its eye over a fantastic FA Cup semi-final.
On target 4
On target 7
Was the result fair?
Over the course of 90 minutes, just about. Chelsea had surging spells but City were the better team overall. Roberto Mancini's side started brilliantly and deservedly led at the break. Aguero's goal was slightly against the run of play and the Premier League champions did well to hold off the Blues' late charge.
Rafael Benitez's side seemed happy to let City have the ball in the early stages and they were made to pay when Nasri drifted into the area unmarked and tucked home after a fortunate deflection. Chelsea came into it after their shaky start, though, and were somewhat unfortunate that City went two up. However, the defending was very slack that allowed Aguero to peel off and head over Cech in off the post. The introduction of Fernando Torres appeared to galvanise the side and they could very well have stolen a goal to send the match into extra time.
A near-perfect first half from City as they had 69% of possession and many more shots than Chelsea. They couldn't resume this dominance after the break, though, as Chelsea roared back into the match. The defensive composure of Vincent Kompany and Matija Nastasic turned out to be just enough in the latter stages and get City to another cup final.
Sports Mole's man of the match
Yaya Toure: The Ivorian has tremendous energy and his powerful drives forward were just immense today. Aguero could have earned this award but his ugly lunge on David Luiz should have earned him a red card and may still do so retrospectively.
Goes to Foy for failing to notice Aguero's horror challenge on Luiz. It would be very surprising if the Argentinian doesn't get punished by the FA.
Not Chris Foy's best afternoon. Somehow he managed to miss Aguero's two-footed jump onto Luiz's backside and also made a couple of other wrong calls, notably failing to award City a free kick when Toure was unbalanced right on the edge of the area.
Chelsea: Next up for the Blues is a trip down the road to face West London rivals Fulham on Wednesday.
City: Mancini's men also have a league game on Wednesday, they host Wigan Athletic in a rehearsal of the final which will take place on May 11.