It was the first time Rovers had beaten the Owls at home in eight attempts in a major competition and the winning margin could have been so much wider.
After a blistering first five minutes in which Wednesday looked as if they would overpower their opponents, it was Rovers who took complete charge of the game.
Their passing was superb and Wednesday were left chasing shadows as Doncaster ran rings round them.
It might have been different had James O'Connor been able to cash in on a chance that had been brilliantly created by Michael Gray and Leon Clarke in the fourth minute, but he volleyed over the bar when he should have scored from about ten yards out.
After that there was only one team in it for the rest of the half as Wednesday failed to win a single corner or land a shot on target while their own goal came under siege.
Paul Heffernan and James Coppinger both had shots blocked before Heffernan sliced a golden opportunity over the top in the 15th minute after Coppinger and Richie Wellens had sliced the visitors' defence apart.
Heffernan snatched at another chance in the 27th minute following a rapid breakaway attack with John Spicer and Coppinger combining to create the opening.
But the Irish striker made no mistake four minutes later when he headed home in fine style after latching onto a right-wing cross from Coppinger.
Wellens had a terrific 20-yarder palmed away by Lee Grant in the 36th minute and Heffernan fired just over the top five minutes before the end of a first half in which Rovers had produced some exhibition football.
A brilliant tackle from Mark Beevers denied Heffernan a second goal four minutes after the interval, before Martin Woods missed a gift in the 61st minute when he fired over the top from point-blank range.
But for all their dominance, Doncaster might have had to settle for a point after failing to finish off their opponents and Clarke caused them an anxious moment in the 69th minute when he headed against the bar from Jermaine Johnson's cross.
But it would have been an injustice had the home side not taken all the points after a commanding display.