The Championship side were no match for the Barclays Premier League champions, who responded to last week's title setback with a dominant display at the Etihad Stadium.
Yaya Toure began the procession early on before Aguero added a penalty and a fine finish either side of a close-range Carlos Tevez effort.
It was just the fillip manager Roberto Mancini needed, with City 12 points behind Manchester United in the title race and amid fresh speculation over his position.
Leeds offered little and their fans' disillusionment with their manager Neil Warnock and their predicament, as they struggle to launch a play-off push, was evident.
Mancini's men gave them little room for manoeuvre. Angered by last week's dismal and costly loss at Southampton, the Italian kept his word and made changes.
The Italian made six in all, although the absences of goalkeeper Joe Hart and midfielder Gareth Barry had nothing to do with their high-profile errors at St Mary's.
Hart was rested in keeping with previous cup ties, allowing deputy Costel Pantilimon an opportunity, while Barry had a knock.
Kolo Toure and Matija Nastasic returned at the heart of defence and Aleksandar Kolarov featured at left-back but Leeds were unable to test them for the large part.
England midfielder James Milner came in to face the hometown club that launched his career while Tevez was restored in attack alongside Aguero.
Under-fire Warnock also made a goalkeeping change, replacing Paddy Kenny with Jamie Ashdown, and brought back former Liverpool man El-Hadji Diouf, Rodolph Austin and Aidan White, but to no effect.
Tevez and Sergio Aguero were lively up front and caused constant problems while Yaya Toure dictated midfield and Milner gave the team he still supports little respite.
The only Leeds player to make his mark on the hosts early on was former City midfielder Michael Brown, who was constantly at the heels of his opponents and looking to irritate.
Such was City's clear superiority it came as no surprise when they opened the scoring with just under five minutes gone.
David Silva was involved in a neat move before Yaya Toure exchanged passes with Tevez on the edge of the box and then went through on goal and expertly took the ball round Ashdown.
Brown caught up with Yaya Toure three minutes later, tangling with the City talisman near the halfway line, but referee Mark Clattenburg stepped in to avert a flashpoint.
City went back on the attack and cut Leeds open with ease as Pablo Zabaleta released fellow Argentinian Aguero and another compatriot in Tevez fired narrowly wide.
It seemed the Leeds defence could not cope with Aguero and Tom Lees gave him the opportunity to double the lead when he pulled him back in the area.
Aguero finished emphatically from the spot and City, comfortable, began to stroke the ball around with even greater confidence.
Leeds showed little bite and, when they did, it came some while later after Brown clipped Tevez.
Kolarov's free-kick was deflected into the side-netting and Javi Garcia got forward to glance a header across goal from a corner.
Leeds belatedly tested Pantilimon when Ross McCormack forced the Romanian to palm away a free-kick in the last minute of the first half.
Brown was removed at half-time by Warnock, depriving the Leeds fans of one figure they love to hate but they turned their sarcasm on their unpopular manager.
They were soon doing that from a position of 3-0 down as Aguero combined with Silva and raced into the box before clipping a ball across goal for Tevez to volley in from close range.
There was little to entertain in most of the second half, although the Leeds supporters maintained their humour by cheering anything forward-thinking their side did - such as Austin shooting well wide - as if they had scored.
Despite that their message was clear: they want Warnock out and they remain unhappy with the team's inconsistency and the club's unclear off-field picture.
Jack Rodwell came off the City bench and almost made an immediate impact as he headed onto the crossbar after Ashdown had parried a Yaya Toure shot.
The fourth City goal came after 74 minutes as Silva split the Leeds defence with a superb pass and Aguero turned and waited for the optimum moment to curl past Ashdown.
Another City substitute, Edin Dzeko, brought a good low save out of Ashdown as City cantered to victory.