Aleksandar Kolarov's spectacular free-kick put City on their way, before Edin Dzeko netted either side of half-time to wrap up the win and ensure that a solitary reply from Lloyd Dyer was of scant consolation to the hosts.
It took just eight minutes for the Blues, who put six past Arsenal on Saturday, to get back on the goal trail, with Kolarov firing a 30-yard thunderbolt into the top corner past a helpless Kasper Schmeichel.
The Foxes goalkeeper helped to keep the score down as City swept forward, but he could do nothing to prevent Dzeko nodding home from close range on 41 minutes after he had been picked out by a clipped cross from James Milner.
The same combination helped City to add a third in the 53rd-minute, with Milner cutting the ball back for an unmarked Dzeko to drill low from 12 yards out.
Leicester were able to pull one back 13 minutes from time but Dyer's strike, which flicked off Vincent Kompany to beat Joe Hart at his near post, failed to spark a dramatic fight back.
The only obvious downside for City, who now have semi-finals to look forward to in January, was an injury to Pablo Zabaleta.
The Argentinian limped off with what appeared to be a hamstring problem early on to join fellow right-back Micah Richards on the casualty list.
Manuel Pellegrini could now have a problem in the position for a Christmas programme that includes a home clash with Liverpool on Boxing Day.
It soon became apparent that the Premier League side, for all Leicester's enthusiasm, were a cut above, even at half-pace.
Schmeichel was exposed all too easily and but for the Leicester keeper, against one of his father Peter's former clubs, the visitors may have inflicted more damage. Jack Rodwell first tested him from inside the area after combining nicely with Dzeko.
Schmeichel could do little to keep out Kolarov's superb free-kick after eight minutes, the Serbian curling into the top corner from 30 yards after City had broken from deep.
Leicester responded well but were unable to find the final ball.
One promising break was ended crudely when Jesus Navas bundled over Dyer but generally City, well marshalled by Kompany, looked to have ironed out recent vulnerabilities.
Gradually the chances began to come for City as Dzeko had a shot blocked, Rodwell screwed wide and a fierce Kolarov drive was punched behind by Schmeichel.
Kompany had a header from a corner blocked, Rodwell curled another shot wide and David Silva also missed the target.
Dzeko went very close to a second as he turned outside the area and curled a left-foot shot millimetres wide of the far post.
The Bosnian finally got on the scoresheet four minutes before the break as headed past Schmeichel from a well-weighted Milner cross.
Milner and Navas then both brought further saves out of Schmeichel before the interval.
Schmeichel was in action again, saving from Dzeko, within moments of the restart but he could not prevent him scoring again for long.
Milner again cut through Leicester on the left and Dzeko turned in his cut-back at the near post past an unsighted Schmeichel, who made his anger with the defence clear.
At the other end Hart had hardly been troubled, although he did need to keep out one Andy King effort.
Silva then tested Schmeichel again before leaving the field, but things hardly threatened to ease up for Leicester as Samir Nasri took his place.
Yet Leicester did manage to finish with a flourish and Dyer took in a ball from Paul Konchesky and lashed in a shot which took a wicked deflection off Kompany and beat a wrong-footed Hart.
Substitutes Matty James and Jeff Schlupp also gave Hart some shots to save but Leicester were unable to set up a frantic finale.