A crowd of 17,888, including nearly 2,500 Rovers supporters, saw a competitive derby settled by the 19-year-old left midfielder's clinical finish, curling the ball into the net with his right foot after Steve Mildenhall had saved from Jay Emmanuel-Thomas.
Man-of-the-match Emmanuel-Thomas rocketed City ahead in the 12th minute with a 25-yard left-footed screamer that arrowed into the top corner following an incisive pass by Bobby Reid.
But Rovers were more competitive after the break and Mark McCrystal rose in a crowded box to head home Lee Brown's free kick just before the hour mark.
Even after Bryan's 76th minute goal, Rovers had a great chance to level,
Oliver Norburn shooting over after Elliott Parish had parried an Ellis Harrison shot. And in injury time City full-back Brendan Moloney headed just wide of his own goal.