Rovers suffered defeat in the Under-18s Premier League Cup to leave their hopes of progressing in the competition hanging by a thread.
The hosts got off to a great start as Cole Palmer scored from close range after an excellent run and cross from D'Margio Wright-Phillips found the attacker lurking in the area.
City could and should have added to their lead, and Rovers punished the home side for their wayward finishing with an equalising goal midway through the first half.
Luke Brennan swung in a cross which was met by Vilius Piliukaitis who, after seeing his initial shot strike the bar, made no mistake with the rebound.
And that was how the scoreline stayed at half time, despite City having the better of the late stages.
Rovers improved after the break, and Louie Moulden had produced a wonder save to deny Brennan, before City launched a devastating counter-attack to retake the lead.
Ryan Corrigan played in Jayden Braaf and his low drive was met by Lewis Fiorini who made no mistake from close range.
Rovers responded well though, and almost drew level on 70 minutes when Jack Vale’s powerful shot struck the bar and bounced back off the line.
Billy Barr's side continued to press for a second equaliser of the day, but it was City who killed the game off with 18 minutes remaining as Palmer's pass found Braaf, who excellently fired home to earn the win.
Manchester City U18s: Moulden, Ogunby, McDonald, Amankwah, Corrigan, Hodge, Knight, Palmer (Dele-Bishiru, 87), Wright-Phillips (Doyle, 40), Braaf, Fiorini.
Unused substitutes: Oduroh, Slicker, Simmonds.
Goals: Palmer, 3, Fiorini, 64, Braaf, 72
Rovers U18s: Eastham, Pike, Garrett, Wilson, Boyomo, Barnes, Durrant (Connolly, 65), Whitehall, Vale, Brennan (Zimba, 65), Piliukaitis (Connell, 55).
Unused substitutes: Winterbottom, Burns.
Goal: Piliukaitis, 23