But the hosts took the lead when Will Atkinson set up Chris O'Grady, with the on-loan Oldham man stabbing the ball past goalkeeper Barry Roche at the second attempt.
Atkinson had a great chance to double the lead when he raced through in the 20th minute only to fire wide of the near post. But the second goal arrived within 60 seconds, as O'Grady fed Chris Dagnall, who danced around Roche before slotting into the unguarded net.
And it was game over when Tom Kennedy's cross was headed home by Atkinson in the 72nd minute, before Curtis grabbed what proved to be a consolation for Morecambe.
Atkinson rounded off the victory in the 87th minute when Roche was unable to keep out his clever backheel flick.