With a strong wind at their backs, the visitors dominated proceedings early on and went ahead when striker Ambrose charged down an attempted clearance by goalkeeper Dean Henderson, one of the Reds’ changes, and calmly slotted home.
United struggled to get out of their third in the early exchanges but grew as the half wore on, albeit without creating any real chances of note. City, meanwhile, went close through Brandon Barker and Olivier Ntcham, while Nicholas Ioannou made a last-ditch tackle to thwart Ambrose.
The wind continued to play havoc after the break but, though it was now more in the home side’s favour, City continued to threaten, with Kean Bryan’s shot deflected wide and Barker seeing an effort blocked by Henderson, who responded well after his early error.
With the score still only 1-0, United sensed an opportunity and Joe Riley’s free-kick drew a first real save from Billy O’Brien, with Ioannou firing the rebound into the side-netting.
There was a delay as Denzeil Boadu was stretchered off following a tackle by Reds midfielder Sean Goss, and soon after substitute Ruairi Croskery had United's best opening with a goalbound shot that was just blocked.
But that proved to be the Reds’ final chance and City wrapped up their 13th consecutive win in injury-time as Ambrose ran on to a through-ball to finish well.
United: Henderson; Evans, Barber