United were also indebted to goalkeeper Wes Foderingham for ensuring that the scoreline was not far, far worse as he made a number of impressive saves to prevent the scoreline being even worse.
United actually took the lead in the game, Sander Berge heading home a good cross from Conor Hourihane.
But a poor goal to concede helped City get back on level terms, and things only went downhill from there from a Blades perspective.
They were perhaps fortunate to go in at half-time level, but City begun the second half as they had ended the first and ran out convincing winners, with Callum O’Hare particularly influential and Viktor Gyokeres giving United’s defenders an afternoon they’ll want to quickly forget.
Foderingham was the only player to come out with any real credit – click through our photo gallery to see how our man rated United’s players ...
1. Wes Foderingham 6
Left terribly exposed for City's opener but made a good save from the scorer, Gyokeres, to stop it being 2-1 to the hosts before half-time. Made at least four more superb stops but was let down badly by those in front of him - strange to give a high mark to a goalkeeper after conceding so many but it could have been much worse without him. Photo: Andrew Yates
2. Ben Osborn 5
A superb challenge early in the second half prevented Gyokores from breaking clear on Foderingham's goal and possibly putting City ahead. Full of endeavour before he was replaced Photo: Ashley Crowden
3. Kyron Gordon 4
Came into the side with Ben Davies struggling with injury, and made a vital block to save a possible City goal towards the end of the first half. But gave O'Hare too much time and space for City's third goal. A harsh reminders of the standard of Championship football Photo: Bradley Collyer
4. John Egan 3
Used all his experience early on to nick the ball away from his man as City started brightly, but was completely overrun like the rest of United's defence as City set about them. Photo: Ashley Crowden