Lincoln hardly had a look in as Rovers gave them the runaround with some slick passing and, if anything, the result flattered the visitors.
Doncaster should certainly have been more than one goal in front at the interval after playing their opponents off the park.
James Hayter and James Coppinger both went close inside the first minute as Rovers set their stall out from the start.
The Lincoln goal led a charmed life with Mark Wilson having a shot tipped around the post by Alan Marriott before Rovers snatched the lead in the 23rd minute.
Coppinger opened up the defence with an incisive pass to James O'Connor who pulled the ball back for Hayter to fire home from close range.
Paul Heffernan and O'Connor missed chances to increase the lead soon after and Wilson had a scorching 25-yarder tipped over the bar in the 35th minute.
Lincoln were rarely able to gain possession such was Doncaster's dominance, although Dany N'Guessan did well to send over a cross from the right which Lee Frecklington headed wide when he should have done better.
Gareth Roberts squandered a good chance and then Coppinger dribbled through to have the keeper at full stretch as Doncaster somehow failed to add to their score until the second half.
Martin Woods rattled the crossbar with a thundering 30-yarder in the 48th minute and Heffernan was twice denied by Marriott before the floodgates opened.
Richie Wellens made it 2-0 in the 56th minute with a curling shot into the top corner after working a clever move with Coppinger and Heffernan fired home from close range five minutes later after Marriott had fumbled a superb cross from Woods.
Substitute Mark McCammon grabbed the fourth in fine style after latching onto a slick back heel from Lewis Guy before Jamie Forrester notched a well taken consolation goal nine minutes from time.