Eric Kinder's side went into the game off the back of a good win over Newcastle United, but goals at crucial times from the Premier Under-21 League leaders saw them claim all three points.
There was little between the sides in the opening period, however the game came to life on nine minutes with a stunning 25-yard strike from Lyle Della Verde that gave David Raya no chance.
Rovers looked to hit back, Will Beesley and Dean Rittenberg going close as the Whites edged the first half.
Rittenberg was denied by David Stockdale just after the break, but a penalty decision on 55 minutes put the home side in control. Moussa Dembele making no mistake from 12-yards after Lasse Vigen Christensen had been fouled.
Again Rovers looked to hit back, showing good attacking instincts, but Tim Payne and Devarn Green efforts didn't trouble the Fulham goal.
In the end the home side added a third to rub salt into the wounds, Della Verde grabbing his second of the night in the closing stages.
ROVERS: Raya, Fernandez, Beesley, Tanner, Edwards, Lenihan (c), Paulo Jorge, Bauress, Rittenberg, Green, Smith
Subs: Pero, Urwin, Payne, Tumwa, Wall.