Forward Modou Cham played a key role in the opening goal and scored a superb second as the young Rovers ran out comfortable winners.
In the Lancashire sunshine the two sides were evenly matched in the opening exchanges but it was Rovers who drew first blood.
Youngster Modou Cham, boosted by a 45 minute run-out for the Reserves the previous week, beat his man in the area and as his shot went past Angus Gunn in goal, the ball was helped over the line by a City player to put Rovers in front.
Midfielders Callum Harris and Ian Vicars went close to doubling the home side's lead but it was a goal of high quality that settled the match in Rovers' favour in the second half.
There seemed little on for Cham as the forward collected Jack Doyle's long throw in the corner, but he cut inside onto his right foot and let fly with a stunning strike that flew into the top corner of the City goal much to the delight of the crowd.
The visitors looked for a way back into the match as the game entered the closing stages but the Rovers defence, featuring two under 16 players in Sam Lavelle and Jack Doyle, held strong and when called upon David Raya made two important saves to ensure a winning result.
Speaking after the game coach Tony Grant said: "The boys did ever so well and we played some good football. It was a whole team effort and very much deserved against a good footballing City side.
"We had a lot of under 16s involved and everyone played their part, Brice Wassi was very good at right back whilst Sam Lavelle impressed once more."
ROVERS: Raya, Wassi, Lavelle, Butterwick, Doyle, Anderson, Torres, Vicars, Harris (sub Tanner 84 mins), Cham, Green (sub Wall 86 mins).
Subs not used: Scott, Joel.