Manchester City reached the League Cup semi-finals for the fourth time in seven seasons by easing past Hull City.
Wilfried Bony steered in the opener, pouncing on a rebound off the post.
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.
Toothless 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 by Derby – their first loss in 14 matches going back to early September.
But until Robertson’s marvellous goal, where the Scotland international started the move inside his own half before finishing following a neat one-two, they rarely troubled home keeper Willy Caballero.
Hull winger Robert Snodgrass came on for his first appearance since August 2014 following a serious knee injury
Silva lining for De Bruyne-inspired City
Spain midfielder David Silva made his first start for Manchester City since 3 October following an ankle injury, returning to captain the home side against Hull.
And the 29-year-old impressed with his usual touch and poise, as well as linking up with Belgium international De Bruyne to great effect.
While Silva pulled the strings, De Bruyne provided the punch.
The Belgium attacking midfielder continues to dazzle since arriving from German side Wolfsburg, taking his tally to nine goals and eight assists in 15 matches for the Blues.
Back to league action for these two high-flying teams.
Premier League leaders Manchester City go to 12th-placed Stoke City on Saturday, while Championship promotion hopefuls Hull visit Yorkshire rivals Leeds United.
Manchester City manager Manuel Pellegrini:
“The most important thing was to qualify for the semi-final but after that it was important for David Silva to have 80 minutes after a long injury.
“It was important for Bony to have 65 minutes after a muscle injury and for Kelechi, a young player, to score.
“I am very pleased because I think it was a difficult game against a good team that is at the top of the table in the Championship.
“More than that we played the third game in less than one week and we had a very good response from the team with different names.”
Hull City manager Steve Bruce:
“If we needed a reminder how cruel it was to play against the big boys, we just had one.
“After 80 minutes we just had our best spell of the match and after 87 minutes it was 4-0. It was never a 4-1.
“Defensively, apart from the goal, I can’t remember them creating a chance in the first half even though they had huge possession.”
Stats you need to know
Manchester City have lost just one of their last 10 meetings with Hull in all competitions, winning six and drawing three
The Blues have scored four goals or more in five of their last six League Cup games at Etihad Stadium
Hull’s only victory in any competition at Manchester City came in the FA Cup in 1930. Since then, they are winless in 10 visits having drawn three and lost seven