Arsenal, protecting an unbeaten home record against City that stretched for 36 years and encompassed 28 games, were the superior side in a contest between two much-changed teams, but after being denied by some superb goalkeeping from Costel Pantilimon were undone by a ruthless finish from Aguero after 83 minutes.
Though Arsene Wenger will be able to glean plenty of positives from the performance, notably the form of young midfielders Alex Oxlade-Chamberlain and Francis Coquelin, Arsenal were still deprived of a sixth semi-final appearance in nine seasons after being punished by Roberto Mancini's vastly more expensive side.
Prior to the match a minute's silence was held in memory of deceased Wales manager Gary Speed but the crowd broke out into spontaneous applause and chants of "one Gary Speed" as the 60,000 in attendance at Emirates Stadium paid tribute to a man who made such a contribution to British football.
Though both sides made widespread changes for the contest, Arsenal's starting XI had the rawer look to it. Any inexperience did not show in a first half that showcased the best of some of the young hopefuls in Wenger's squad.
Oxlade-Chamberlain, named as an outside contender for the Euro 2012 squad by Fabio Capello this season, was a persistent threat from right midfield, while Emmanuel Frimpong and, in particular, Coquelin outshone the more senior Owen Hargreaves and Nigel De Jong in the centre of midfield.
It was Coquelin who created the first good chance of the tie when his excellent first-time cross flew across the face of the box and found Park Chu-young at the back post. However, the South Korean was denied by a tremendous save from Pantilimon as he flung out his left arm and clawed the ball out.
The Romanian keeper, making only his third appearance for City, excelled again on 28 minutes. Oxlade-Chamberlain exchanged passes with Marouane Chamakh before unleashing a fearsome effort from 25 yards that was flying into the top corner before Pantilimon touched it over the bar.
City had threatened themselves when Adam Johnson cut in past Ignasi Miquel from the right and fired an effort just over the bar. However, City looked sluggish and Mancini responded by removing Aleksandar Kolarov, stationed in an unfamiliar left-wing role, and replaced him with Aguero.
Samir Nasri, booed on his first return to Emirates Stadium since departing in divisive circumstances in the summer, thought he was the man to be hooked and looked only too ready to leave the pitch, but was ordered to stay on as Kolarov made way.
City's tactical tinkering tightened things up and Edin Dzeko enjoyed two good chances in the first 15 minutes of the second half, the first and better of which saw him collect the ball 20 yards from goal, spin to face the target and then curl an effort just wide of the post.
Arsenal continued to impress with their application, particularly given the vast disparity in how much the two teams cost to assemble, and Oxlade-Chamberlain tested Pantilimon with another effort, though his shot from 20 yards lacked pace.
Dzeko rose above Sebastien Squillaci to head wide as City carved out a rare chance but Arsenal's exuberance got the better of them with seven minutes remaining.
With men committed forward for a corner, Arsenal were caught on the break as Dzeko powered forward and fed Johnson with a quite sumptuous pass through the middle of the pitch. He turned the ball into the path of Aguero, who slipped a shot past Fabianski with ease.
The scoreline was harsh on Arsenal and they almost equalised in the dying seconds when Chamakh only just failed to get on the end of a cross from substitute Gervinho, but Wenger's side were doomed to their first defeat in 11 games.