A home win and safe passage through to the quarter-finals was never really in doubt after an early team move was finished by Yaya Toure and Sergio Aguero earned and converted a penalty within the first 15 minutes.
From that moment on City controlled the possession and territory in the main and, in the second half, Carlos Tevez scored from close range before Aguero grabbed a second, floating the ball off the far post and in.
Roberto Mancini made six changes to his side, including dropping Joe Hart to the bench after publicly criticising the England goalkeeper following last week's defeat to Southampton, whilst Aguero and Tevez were paired in attack. Neil Warnock chose to bench new signing Steve Morison, whilst Jamie Ashdown was brought in for Paddy Kenny in goal, something Leeds have done regularly in cup competitions this season.
City started the stronger, and were ahead after just five minutes as they looked to make amends for recent poor displays. Tevez, David Silva and Yaya Toure combined sharply on the edge of the area and, when the latter found space in the box, he waltzed past Ashdown and stroked the ball home to give the hosts the perfect start.
The home side continued their dominance, and 10 minutes later doubled their lead. Aguero ran at Tom Lees outside the six-yard box, and the young defender blocked the Argentine's path before the City striker himself stepped up and placed the ball into the top left hand corner of the goal.
Although the first half fell into a natural lull with City so comfortable, it was the Premier League champions that had the monopoly on chances at goal. They forced a series of corners, from which Silva rifled wide and Aleksander Kolarov forced Ashdown into a save low down at his near post.
City's best chance to extend their lead before half-time fell to Yaya Toure, who sent a dipping volley towards goal from 25 yards, but again Ashdown was equal to it as Leeds struggled to gain a foothold.
If Leeds hoped that the second half could be more fruitful, the wind was taken from their sails just seven minutes after the restart. Aguero attacked the touchline before crossing across goal for Tevez, who was less than a yard out and bundled the ball home via a knee to end the game as a contest.
Mancini took the opportunity to give vital playing time to both Jack Rodwell and Maicon, as City were able to effectively play at their own pace. Tevez's last action was to just fail to connect with a squared ball from Aguero, and Milner then fired wide from distance. Rodwell headed against the bar after a Yaya Toure shot had been palmed away, but in truth it was easier to score and he should have done better.
Leeds' first real chance came with 20 minutes remaining, Luke Varney heading over from eight yards under pressure from Nastasic.
Aguero then grabbed his second of the game after being found in acres of space before knocking the ball past Ashdown and in via the far post, and Leeds moved into damage limitation mode.