Neil Wood's side came from behind, after Alfie May's 61st-minute opener, with Ethan Galbraith rattling home a piledriver of a volley before Mason Greenwood struck deep into stoppage time to earn all three points.
Greenwood and Tahith Chong both started for United, who were, nonetheless, missing some key players at this level. It perhaps showed in the opening exchanges, with Rovers piling on the pressure and testing Matej Kovar in the visiting goal.
Madger Gomes had the first shot of the game, as early as the third minute, and, although Kovar saved comfortably, his next stop, to deny May, was a top reflex movement with with his leg.