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 ...
5. Jack Robinson 3
Had a nightmare with City's opener as he was caught under the flight of a long punt forward and missed his header, allowing Gyokeres a clear run at goal to score. Almost culpable for another when he was robbed in his own area but Foderingham saved well Photo: Simon Bellis
6. Rhys Norrington-Davies 4
Had a good early crossing chance after Berge and Hourihane combined, but he ballooned his cross high over Moore's crossbar. That sort of set the tone for his afternoon from then on in Photo: Ashley Crowden
7. Ollie Norwood 4
Taken off for McBurnie with the damage already long done. United's midfield couldn't assert any sort of control for long enough and they were swarmed all over by City Photo: Ashley Crowden
8. Conor Hourihane 4
Great cross picked out Berge expertly for the big man to head the Blades ahead, but other really memorable moments were few and far between from an international midfielder Photo: Andrew Yates