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 they reached the EFL Cup final.
Tougher tests will await than that presented by Burnley at the Etihad Stadium on Saturday, 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.
What does it mean? Four trophies still up for grabs
It remains a possibility for City to complete the clean sweep of silverware. Few would bet against them in the EFL Cup and, on this showing, the FA Cup could easily come their way. Of course Liverpool will take some catching in the Premier League, while the Champions League would be a first for the club, but can you really discount this City vintage from claiming the lot?
De Bruyne the key to unpick any lock
Guardiola is blessed with options in his squad, but few players in the world could satisfactorily fill the void created when De Bruyne is absent, as he has been for large parts of this season. The Belgium international is such a creative driving force and Burnley simply could not live with him.
Vydra fluffs his lines
It may seem harsh to single out for criticism a lone striker who received so little service, and indeed whose only chance came from his own willingness to close down a careless Otamendi. However, having forced such a clear-cut opening at the start of the second half, Vydra simply had to score. He instead shot wide, and five minutes later it was practically game over.
Key Opta Facts
- City have scored 29 goals since they last conceded; they have not let in a goal in 566 minutes of play since Roberto Firmino equalised for Liverpool at the Etihad Stadium on January 3.
- Jesus has scored eight goals in all competitions in 2019, at least twice as many as any other Premier League player (Fernando Llorente, 4).
- City have scored 28+ goals over a period of six games in all competitions for the first time since January 1939 (also 28).
- Aguero has scored in all five of his appearances against Burnley at the Etihad for Manchester City, netting six goals in total.
It is a quick turnaround for both clubs as the Premier League retakes centre stage on Tuesday, with City heading to Newcastle United and Burnley returning to Manchester to face in-form United.