There was little to chose between two hard-working League One sides in a closely-contested first half at the Keepmoat on Saturday, but Rovers grabbed the lead following an own goal blunder when Christian Ribeiro chested the ball into his own net under pressure from Martin Woods as he attempted to clear a terrific right-wing cross from David Cotterill.
Scunthorpe worked tremendously hard in the first half with Mark Duffy and Jimmy Ryan going close, but the game was one-sided when Rovers made it 2-0 straight after the interval.
Cotterill fired home after on-loan goalkeeper Steve Mildenhall had palmed a cross from Iain Hume straight to his feet.
Rovers' skipper and former Iron defender Rob Jones made it 3-0 with a towering header following a 62nd-minute corner and Billy Paynter added the fourth with a cracking 20-yard shot a couple of minutes later.
It might have been more, but Chris Brown had a header cleared off the goalline and Mildenhall made a reflex save from Dave Syers in the closing stages.