A three-goal blitz inside 11 first half minutes from Andy Butler, Liam Mandeville and Matty Blair set Rovers on their way to a fourth straight league win.
Stevenage launched a second half comeback with goals from Tom Pett and Fraser Franks before top scorer John Marquis claimed his 11th goal of the season.
Substitute Rowan Liburd then pounced from close range and Rovers had to survive a nervy finish to record their fourth straight league win - one which sent them top of the division and, more significantly, eight points clear of fourth spot.
Darren Ferguson named an unchanged side for the third successive game, with Andy Williams returning on the bench.
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Stevenage were uncompromising in their approach from the outset and as a result Rovers initially struggled to stamp their authority on the game.
However, they did carve out a couple of decent openings during a tight opening quarter, two of them falling to Tommy Rowe who chipped one effort onto the roof of the net.
Rovers looked good when they got the down and played but they broke the deadlock on 28 minutes via a set piece. James Coppinger curled over a free kick from the right and Butler got in front of his man to plant a header past Jamie Jones.
It proved to be the cue for a stunning three-goal blitz inside 11 minutes as Doncaster demonstrated a real clinical edge in the final third.
On 35 minutes Rovers neatly worked the ball to the right of the area where Mandeville drilled home with aplomb.
And four minutes later more good build-up play down the left ended up with the ball falling nicely for Blair, who spectacularly volleyed in from the edge of the area.
It took half an hour for Stevenage to register their first shot on goal, a rare piece of hesitant defending from Rovers allowing Ben Kennedy to shoot straight at Marko Marosi from 20 yards.
Marosi played his part in a superb first half, though, at 2-0 helping to keep out a downward header from Charlie Lee with a low save after the ball struck the post.
Stevenage began the second half in positive fashion as substitute Pett tested Marosi's handling and Dean Wells volleyed onto the roof the net.
The home side got their reward just after the hour mark when a quick break ended with Pett powerfully firing home.
Rovers could and maybe should have restored their three-goal cushion immediately. Firstly Coppinger drilled a cross right across the face of goal before Marquis got in on goal but dragged his shot well wide.
It then looked like a nervy finish was in store when Fraser Franks further reduced the deficit on 72 minutes with a stunning chest and volley from distance.
But just a minute later Marquis rose to head home a free kick, although the final touch may have come off Stevenage goalkeeper Jones.
Liburd then did set up a tense finish when he prodded home following a corner, before Pett curled an effort inches wide - but Rovers held on for a thrilling win.
Stevenage: Jones, Henry, Wells, King, Francis, German (Pett 46), Schumacher (Liburd 70), Lee (Tonge 46), Cowans, McKirdy, Kennedy. Subs not used: Day, Kerr, Slater, Wilmott.
Rovers: Marosi, Alcock, Baudry, Butler, Mason, Houghton, Blair, Rowe, Coppinger (Williams 84), Mandeville (Keegan 73), Marquis. Subs not used: Jones, Evina, Calder, Beestin, Wright.
Referee: Lee Collins (Surrey)