Both teams had made sweeping changes, but despite plenty of industry from Arsene Wenger's young side - with Alex Oxlade-Chamberlain again producing an impressive display - it was big-spending City who had the edge as £35million Argentina striker Aguero slotted home with seven minutes left following a sweeping counter-attack.
The Premier League leaders will now turn their attentions to securing safe passage into the latter stages of the Champions League next month after the depth of Roberto Mancini's squad again paid dividends.
There was a tribute to late Wales manager Gary Speed, with the away fans spontaneously singing his name followed by applause.
Samir Nasri, on his first return since an acrimonious £24million summer transfer, was booed.
The former Gunners midfielder's first touch was resoundingly booed, before chants of "you only left for the money" rang out around Emirates Stadium.
City winger Adam Johnson's 25-yard effort dipped just over before Arsenal broke down the left through Oxlade-Chamberlain, who fed Marouane Chamakh before the ball was pushed out for Francis Coquelin to whip it back across the six-yard box.
Park Ju-young, who scored in the last round against Bolton, arrived on cue at the far post, only for reserve keeper Costel Pantilimon to make a brilliant reaction save to his left.
The 6ft 8in City keeper was called into action again on 27 minutes when the Romanian - on a one-year loan from Poli Timisoara - made another acrobatic one-handed stop to push away Oxlade-Chamberlain's fierce 20-yard strike which was heading for the top corner.
Laurent Koscielny was alert to knock the ball behind just as Nasri looked set for a tap-in.
Oxlade-Chamberlain continued to be Arsenal's main attacking threat down the right - so much that Mancini made an early change on 32 minutes when he replaced Aleksandar Kolarov with Aguero and switched formation. The Serbian captain looked less than impressed as he slumped into the visitors' dugout.
Arsenal were lively again at the start of the second half, as Oxlade-Chamberlain made more inroads down the right, this time an angled drive beaten away by the City keeper.
Mancini became more animated on the touchline as the visitors failed to make the most of possession, especially when on the break.
Edin Dzeko hooked Zabaleta's cross behind as the Blues maintained their threat before Koscielny made a couple of timely last-gasp tackles.
When Arsenal did work the ball forwards into the City penalty area, Chamakh could only crash an angled drive into the sidenetting.
On 67 minutes, Park was replaced by Ivory Coast frontman Gervinho.
The change gave the Gunners some extra urgency in attack to supplement Oxlade-Chamberlain's tireless running.
Dzeko glanced what was a decent chance wide, before Owen Hargreaves was replaced by Abdul Razak.
Arsenal also made a change for the final 10 minutes of normal time, bringing on Thomas Vermaelen for full-back Ignasi Miquel.
Gervinho scampered away down the right and his low centre was knocked behind away from Yossi Benayoun.
City broke quickly and this time produced a finish worthy of their multi-million pound attack to win the tie with seven minutes left.
Dzeko's long ball split the Arsenal defence, before Johnson brilliantly played in Aguero - and the Argentinian coolly slotted past Lukasz Fabianski.
Arsenal sent on Russian playmaker Andrey Arshavin for Oxlade-Chamberlain in the closing stages as the home side searched for an equaliser, but there was to be no fightback.