The League Two outfit took the game to their Championship neighbours as early as the sixth minute, Lewis Alessandra's strike setting the foundations for a first-round cup shock.
Andy Fleming put the Shrimps firmly in the driving seat shortly after half-time, a two-goal deficit which Ian Holloway's side, beaten play-off finalists in May, could not come back from despite Alex Baptiste's 77th-minute consolation.
It was the first time the Lancashire rivals had been paired together in a competitive fixture and Morecambe got off to a memorable start, Alessandra finding the far bottom corner with a well-struck effort from the edge of the penalty area.
Highly-rated Matt Phillips hit a post as the Seasiders searched for a route back into the game, but the hosts' task was made even harder just 11 minutes into the second half as Fleming converted from 12 yards.
Gary Taylor-Fletcher saw an effort turned around by Shrimps stopper Barry Roche before Baptiste's left-footed finish reduced the arrears from Elliot Grandin's inswinging corner. Phillips hit a post for a second time in the 89th minute but the Seasiders could not force a late equaliser.
Morecambe boss Jim Bentley was purring after watching his side start the new season with the victory away at the club's Lancashire rivals.
Bentley said: "I'm delighted, for a club of our size to come on a coach to our near neighbours and get a win is a special day for the football club.
"I'm delighted for everyone at Morecambe and most of all the supporters who have travelled in their numbers and given us terrific support.
"The fans are massive, they play a huge part. Attendances at home haven't been great, but away from home the following has been superb."