Rovers failed to make their early dominance count as they were undone in the second half at AFC Wimbledon.
Darren Moore's side had a deserved lead at the interval from Kwame Thomas' header, but were unable to convert any other chances.
And despite starting the second period well, the home side were allowed a way back into the game through a penalty for a foul on Marcus Forss - which he converted - before they snatched victory with a quick counter-attack goal converted by Callum Riley.
Rovers opened brightly, with James Coppinger feeding Kieran Sadlier who forced the home goalkeeper Nathan Trott into a safe inside the opening 30 seconds.
Trott was by far the busier of the two keepers in the opening period, having to get down quickly to his right to stop Ben Whiteman's effort after neat play between the Rovers captain and Thomas in the fifth minute and he could watch on 60 seconds later as Sadlier lifted an effort over.
Rakish Bingham forced a scrambling save from Trott when he latched onto Thomas' knock-on, and from the resulting corner the visitors went ahead. Left-back Reece James' delivery was inch-perfect for Thomas, who was barely challenged as he headed in powerfully at the far post to give Moore's side the lead their performance clearly merited.
Rovers were buoyed by the strike, and Thomas was not far off doubling the lead a minute later when he got on the end of a corner deliver from the other side sent in by Coppinger.
Trott was peppered with shots, with Ben Sheaf - who was fouled in the build-up to the chance - getting a shot away which was comfortable for the home keeper to hold.
And when the referee pulled play back for the foul on Sheaf, Sadlier tried his luck with a powerful effort which the home keeper was relieved to collect up at the second attempt.
The home side did not look threatening in the opening spell of the game, with Paul Osew winning a corner after 21 minutes the most the home side had to cheer about. Terrell Thomas headed Max Sanders' cross from the resulting set-piece well wide.
The Dons' second corner also produced an opportunity as Cameron John's flicked header did not clear the box, with Rod McDonald blasting an effort into the fans behind the goal.
Rovers responded by quickly getting forward, with Reece James given an inviting amount of space in an advanced position. His low left-footed shot went just wide of the far post.
Set-pieces looked to provide the home side with their best opportunities, with Terrell Thomas again heading wide on the half-hour mark. The game became a bit scrappier as it approached half-time, with a Whiteman half-volley going wide as Rovers tried to step it back up again.
And Sheaf should have made it 2-0 just before the break when he picked up Sadlier's flick-through, but his shot was not powerful enough to test Trott who was well positioned to collect the ball.
There were no changes from either side at the break, with Rovers again starting brightly with a Whiteman header ricocheting off a home defender after 52 minutes.
But the home side were given an opportunity to get back into the tie when Donervon Daniels fouled Marcus Forss in the area. The Dons forward dusted himself up to score from the penalty spot, sending Seny Dieng the wrong way.
Rovers boss Moore sent on Jon Taylor on the hour mark, replacing Bingham, and he caused problems down the eight after 67 minutes only to see his pull back intercepted.
There were appeals for handball when Whiteman had a shot blocked by Terrell Thomas. And Rovers' frustration was compounded as the home side countered quickly, with Forss getting the better of Brad Halliday then feeding Riley to slam the ball home.
That prompted even more pressure from Rovers. Taylor sent a low effort just wide of the far post after a great move saw James pull the ball across from the left wing.
James had a couple of shots from inside the area - the first was off target, while the second rattled around a few bodies in the area before being cleared.
The best chance for a leveller came when Whiteman spotted Coppinger's run and lifted the ball over the backline to find him. Coppinger just could not keep his shot down.