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.