Rovers five-match unbeaten run was ended by Rochdale, as the home side could not convert numerous second-half opportunities in this Emirates FA Cup third round clash.
Calvin Andrew’s first-half header, as he flicked home a set-piece, was the difference between the two sides.
After a slow start to the game, with both sides having little to show for, it was the visitors who took the lead.
Bunney’s free-kick was met at the back post by Andrew, who headed home into the corner for the opener.
Rovers did edge their way back into the game as the half progressed, and came close to equalising just after the half-hour mark.
Rodney Kongolo’s ball in from the right was met by John Marquis in the middle, but his strike was straight at Josh Lillis who could claim comfortably.
Matty Blair was next to try his luck for the home side, as Mason’s ball in was cleared out to the right-back, but his shot from 25 yards out was saved by Lillis once more.
Ian Lawlor then had to be alert to prevent Dale from doubling the lead on the stroke of half-time, as Bunney’s cross from the left almost crept in at the far post, but the Irishman got across well to tip around the post.
Rovers came out firing after the break and went very close to taking the lead within 10 minutes of the interval.
Rowe’s cross into the box was met by the un-marked Alfie Beestin, but Lillis superbly denied the youngster from close-range, before a scramble in the area lead to Blair’s follow-up shot being blocked by Bunney.
Rochdale went on the attack themselves, and almost extended their lead.through their captain.
The Rovers’ defence thought they had cleared the ball away from danger, but they could only tee up Ian Henderson, who struck a volley past Lawlor’s far post.
Bunney then went close again for the visitors, as his left-footed drive whistled past the post, in what was a real let-off for Rovers.
Rovers again came forward, though, and went agonisingly close to levelling the score.
Kongolo’s hard work and neat turn down the right saw him play the ball inside for Marquis, but the striker’s shot from the edge of the area cannoned back off a post.
A Rovers free-kick then found Rowe down the left, and his cross into the box was met by the head of the rising Andy Butler, but he could only guide his header wide of the far post.
Rowe was causing a lot of problems down the left-hand side, and he was in behind again after playing a one-two with Coppinger, but fired just over as Rovers tried desperately to stay in the FA Cup.
Rovers return to league action next weekend, with the visit of Plymouth Argyle to the Keepmoat Stadium in Sky Bet League One.