After an even opening, two goals within five minutes left United facing an uphill battle. Jordy Hiwula latched onto a through ball by Albert Rusnak and clipped his finish past Liam Jacob before Rusnak dribbled through to bag a fine solo effort to double the lead.
There was a real blow when powerful skipper Luke McCullough was forced off after a clash of heads with Hiwula and, with no defender on the bench, Ben Pearson's introduction meant a reshuffle of the team.
Paul McGuinness' side still responded to reduce the arrears when a Joe Rothwell cross was only cleared to Gyliano van Velzen and the Dutchman calmly placed a relaxed finish past City keeper Angus Gunn.
In a game of few other chances, the second half was littered with free-kicks and swung in City's favour when a hugely debatable penalty was awarded for a challenge by Luke Hendrie on Rusnak as he shot wide. Rusnak took the spot-kick himself and slammed it past Jacob to put the game beyond the hosts' reach.
Andy Cole, who was on the touchline, saw his son Devante come on as a substitute for City but there were few late openings for either side as the Reds, who also lost Tom Lawrence through injury, failed to really test Gunn again.
United: Jacob; Hendrie, McCullough (Pearson 35), Dalley, Blackett; Barmby, Rothwell, Enkangamene, van Velzen (Gorre 82); Lawrence (Daehli 74), Byrne. Subs not used: Coll, Rudge.