An early goal from Wilfried Bony should have been the platform for a comfortable win, but it was not until a strike from 19-year-old substitute Kelechi Iheanacho and a Kevin De Bruyne brace in the last 10 minutes that the match was wrapped up.
Hull left-back Andrew Robertson scored an even later consolation but, in truth, three-time winners City were not really stretched at any point, with their superior fitness taking effect in the latter stages.
“We only had 72 hours to recover [from the 3-1 league win over Southampton] so it was a very good answer from all the squad,” City boss Manuel Pellegrini said.
“The most important thing is to be involved in all the competitions at this stage. We were very solid and we didn’t allow chances for Hull to score.”
Pellegrini made five changes from the win over Southampton, which gave David Silva his first start in two months, and it affected their fluidity.
Even the goal came from a Hull mistake, although there was no doubting the quality of De Bruyne’s shot which cannoned back off the post into the path of Bony, who could not miss an empty net.
Hull, fourth in the Championship and with their sights set on a return to the Premier League, made seven alterations from the defeat at Derby and that affected them even more.
There was no energy, no competitiveness, no outlet and no cutting edge with leading scorer Abel Hernandez relegated to the bench.
It led to a stultifying first half broken only by Bony’s 12th-minute goal, which was virtually handed to the hosts when Hull attempted to launch a counter-attack, only for Sone Aluko and Chuba Akpom to leave the ball for one another.
De Bruyne did not need a second invitation and although his effort hit the post Bony was on hand to finish it off.
Conceding did little to rouse Hull from their slumber and it was not until two minutes before half-time they threatened in the opposition penalty area, but Akpom’s promising diagonal run was not matched by the weak finish.
Hull goalkeeper Eldin Jakupovic could only bat away another long-range De Bruyne shot after the break, but this time Bony failed to take advantage and Jesus Navas flashed a shot against the outside of the post.
The Tigers sent on midfielder Mohamed Diame and top-scorer Hernandez with the game technically still in the balance, but it was the introduction of Raheem Sterling which proved decisive as his 80th-minute cross was turned home by fellow substitute Iheanacho.
De Bruyne took advantage of widening gaps in Hull’s defence to score his first and then whipped in a free-kick, meaning he has now been involved in 16 goals in 11 home matches for City.
Robertson’s goal in added time at least gave the 5,000-strong travelling support something to cheer.
Caballero, Sagna, Otamendi, Mangala, Clichy, Fernandinho, Delph, Jesús Navas (Sterling 62), Silva (Demichelis 83), De Bruyne, Bony (Iheanacho 71).
Jakupovic, Odubajo, Maguire, Bruce, Elmohamady, Livermore, Hayden, Taylor (Diame 58), Robertson, Aluko (Snodgrass 73), Akpom (Hernandez 68).