A fantastic run and finish from Sam Burns was enough for Rovers to book their place in round five of the FA Youth Cup and send Charlton Athletic out of the competition.
Mike Sheron's side weren't at their flowing best on the night, but Burns took one of the few chances in the encounter; running from his own half to beat Nathan Harvey just four minutes before the break at a chilly Ewood Park.
Charlton pressed for an equaliser in the second half, but a mixture of fine goalkeeping from Jordan Eastham and poor finishing ensured Rovers secured their progress.
Sheron made one change to his side from the one that started against Newport County Under-18s in round three, with Zak Gilsenan coming in for Chanka Zimba.
It was an even start to proceedings at Ewood Park, but Rovers had the two opening opportunities of the encounter with Sam Burns prodding wide before Dan Pike sent a first time strike high and wide inside the opening 15 minutes.
At the other end, Euan Williams was a whisker away from opening the scoring just before the half hour, but the effort curled just beyond Eastham's left-hand post.
There were four minutes of the half remaining when Burns put Rovers in front with a terrific run and finish that started in his own half and ended with a low strike that flew beyond Nathan Harvey and into the bottom left-hand corner.
Rovers came out for the second half with the bit between their teeth and went in search of a second goal early after the break, with Luke Brennan forcing Harvey into a fine stop down to his right.
Richard Afrane-Kesey came close to an equaliser for the visitors, with Eastham positioned well to hold onto the forward's attempt at goal just five minutes after the interval.
Aaron Henry went for goal direct from a free kick soon after, but his set piece drifted into the side-netting with Eastham covering just in case.
The Addicks were having the better of the game and Williams tested Eastham with a save that was routine for the Rovers goalkeeper with 15 minutes of the tie remaining.
Frederick Barton missed a glorious chance to send the tie to extra time late on, but Rovers held on to book their spot in round four.
It could have been more comfortable with just seconds remaining, but Burns saw Harvey in his way before blazing the follow up effort over the bar.
Rovers will host Preston North End's Under-18s in the next round, with a date for the fixture to be confirmed in due course.
Rovers Under-18s: Eastham, Pike, Cirino, Saadi, Boyomo, Whitehall (c), Burns, Harlock (Weston, 50), Lonsdale (Zimba, 74), Gilsenan (Leonard, 79), Brennan.
Unused substitutes: Dowling, Wyatt, Gent, Cunningham.
Goal: Burns, 42.
Booked: Harlock, 22, Lonsdale, 73
Charlton Athletic Under-18s: Harvey, Barton, Aidoo (Campbell, 84), Henry, Barker, French, Albon, Agyemang, Santos, Williams (Ladapo 89), Afrane-Kesey (Gavin, 70)
Unused substitutes: Watkins, Buhari, Garande, Reilly.
Booked: Barton, 81.
Referee: Thomas Kirk.