Rovers dominated the first half and deservedly led through Tyrhys Dolan's header, but were pegged back early in the second half by Cole Stockton's confident finish.
And the Sky Bet League One new-boys secured victory over the 2002 winners six minutes from the end when Burnley loanee Adam Phillips emphatically converted a penalty.
Blackburn should have been out of sight after a first half that saw Ben Brereton Diaz blaze over from close range. He was later denied by Jokull Andresson, before Dolan broke the deadlock midway through the half, meeting a teasing Harry Pickering cross with an unstoppable diving header.
Andresson kept the deficit at one goal with a fingertip save to deny Ryan Nyambe and the Shrimps capitalised in the 53rd minute when Stockton hammered home his third goal of the season from Jonah Ayunga's cutback.
The comeback was completed in the 84th minute when Phillips lashed a penalty into the roof of the net after Dolan tripped Greg Leigh to send the visiting fans wild.
Andresson pulled off a stunning save from Sam Gallagher in stoppage time to confirm the result.