Darryl Duffy opened the scoring for the visitors in the 21st minute when he cut in from the right and found the bottom far corner of the net with an excellent finish. It was their first shot on goal, as United had started the brighter.
His strike partner Jo Kuffour made it 2-0 when he too forced his way past an uncertain home defence to squeeze the ball from an acute angle through the legs of goalkeeper Joe Murphy.
It was a real stunner for Scunthorpe who had climbed into the automatic promtotion contention after three straight wins heading into the game.
At the start of the second-half they introduced new loan signing Henri Lansbury from Arsenal.
The teenage England U19 international produced some good touches in his first taste of League football.
The Iron enjoyed plenty of possession but could not make it count. They missed a great chance to get themselves back into the game in the 54th minute when a poorly-struck penalty attempt by Paul Hayes was easily saved by keeper Steve Phillips following a handball by the visiting defender Craig Hinton.
Scunthorpe were out of luck in the closing stages when a good effort from midfielder Grant McCann came back into play off the underside of the bar.
And Kuffour might have made it 3-0 for Rovers when he lifted his shot high over the top when well placed late on.