Jack Redshaw was the Shrimps' goal hero with a close-range finish four minutes from time to seal a fine fightback after going behind.
John-Joe O'Toole fired the visitors into the lead on the half hour. After good work from Lee Brown down the left Matt Harrold turned smartly in the box and forced a good save from Barry Roche but the ball fell perfectly for the midfielder who made no mistake from six yards out.
Rovers should have doubled their lead on the stroke of half time when David Clarkson found himself unmarked 10 yards out but he failed to find the target when he blazed over the bar.
He was made to pay when Morecambe levelled 10 minutes into the second half. Jack Sampson crossed from the right, Stewart Drummond flicked on and Padraig Amond slid in at the far post to score at full stretch.
Sampson was at the heart of Morecambe's winner with a header that hit the post before bouncing back to Redshaw who slotted home his second of the season from six yards.