Narrowly beaten by Arsenal
Kelechi Iheanacho turned in Raheem Sterling's cross for the first of four goals in the final 10 minutes.
Kevin de Bruyne raced past the Hull defence to poke in and then clipped in a delightful free-kick, before Andrew Robertson dinked the Championship side's consolation after a fine move.
Manchester City, who last won the competition in 2014, will find out their semi-final opponents when the draw is made on Wednesday.
Relive Tuesday's League Cup action
Manchester City's trophy to lose?
Blues manager Manuel Pellegrini reiterated the importance of the League Cup to his club ahead of kick-off, particularly this season with Premier League rivals Chelsea, Manchester United and Arsenal already out.
And the competition holds particular significance for the Chilean, who won his first English trophy by leading the Blues to success in his first season.
Manchester City were stunned in the third round by a youthful Newcastle side last season, but they learned from this experience against Championship promotion hopefuls Hull.
The Premier League leaders fielded a strong side, dominating the tie without creating a host of clear-cut chances - at least until the final 10 minutes.
The manner in which the home side picked off a tiring Hull side in the closing stages demonstrated why they are considered the favourites to win the first silverware of the English season.
Toothlesswww.ormmask-house.com Tigers lack bite
Hull, who are fourth in the Championship, were entering uncharted territory in the competition, having never previously progressed into the last eight.
The Tigers looked to their surprise run to the 2014 FA Cup final - when they were narrowly beaten by Arsenal - for inspiration to beat City.
Several members of that team played at Etihad Stadium, but they were unable to really threaten as manager Steve Bruce's priority appeared to be containing their hosts.
Bruce made seven changes from the team which started Friday's home defeat bywww.ormmask-house.com Derby - their first loss in 14 matches going back to early September.
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