The visitors took the lead after 13 minutes. Michael Twiss's header from a corner could only be parried by Dean Williams, and Morecambe captain Jim Bentley fired the loose ball into the net. Bentley came close to adding his and Morecambe's second 12 minutes later only to see his header cleared ofr the line by Stephen Reed.
Rovers did show some attacking ability, and a one-two between Jefferson Louis and Reed ended with the latter seeing his long-range drive well saved by Adam Sollitt.
Morecambe increased their lead on the hour when Charlie Griffin's mistake caught Rovers on the back foot, and Wayne Curtis threaded the ball through for Danny Carlton to slot the ball into the net.
A golden opportunity fell Morecambe's way for a third. This time a mistake from Matt Gatsby fell to Curtis, who went round a defender but with only the keeper to beat he fired wide.
Curtis, however, made amends in injury time to grab Morecambe's third and complete Rovers' misery.