Pep Guardiola described talk of City winning the quadruple as "fantasy", but it remains an attainable achievement for his side at the end of a week in which it reached the Carabao Cup final.
Tougher tests will await than that presented by Burnley at Etihad Stadium in this clash, with the visitors undone by a first-half strike from the in-form Gabriel Jesus and one apiece after the break from Bernardo Silva and Kevin De Bruyne, the latter being the pick of the bunch.
City also won October's Premier League fixture here 5-0 and Sean Dyche's side succumbed to the same fate as Kevin Long's own goal and Sergio Aguero's penalty completed the rout.
The most notable action of the first 12 minutes saw Kyle Walker break a corner flag as he attempted to deliver a cross, leading to a delay in the action as a replacement was sourced.
City should have taken the lead in the next attack, De Bruyne's cross skidding underneath the outstretched leg of the onrushing Jesus.
Silva was next to come close as his side-footed effort was well kept out by an alert Nick Pope, who first parried then caught a subsequent strike from Danilo.
Having snapped the flagstick, Walker's next target was Steven Defour, the England full-back receiving a yellow card for his mistimed challenge on the Belgian.
The breakthrough followed soon after as Jesus cut in from the left side of the area and finished with confidence past Pope for his eighth goal in five matches.
Burnley wasted a glorious opportunity to equalise within three minutes of the restart when Nicolas Otamendi was caught in possession, but Matej Vydra fired wide with only Ederson to beat.
Dyche's men paid the price when Silva's deflected shot doubled City's lead after collecting a pass from De Bruyne, who then lashed in the goal of the match from 25 yards out.
A fine outing from De Bruyne was capped when his cross was turned into his own net by Long, whose mix-up with Pope led to the spot-kick from which Aguero converted.
It is a quick turnaround for both clubs as the Premier League retakes centre stage on Wednesday (AEDT), with City heading to Newcastle United and Burnley returning to Manchester to face in-form United.