Top scorer Jamie Cureton struck twice either side of an Arron Davies strike to gave Paul Tisdale's side an important three points over a Morecambe side unbeaten at the Globe Arena since September.
Cureton sparked the victory with a fine goal in the 62nd minute when he beat Will Haining to Tommy Doherty's superb through ball and slid an effort past Shrimps' keeper Barry Roche from just inside the box.
The second goal came four minutes from time when Jimmy Keohane found space down the right and crossed to the far post for Davies to slide the ball past Roche from 12 yards out.
Cureton put the gloss on a historic result two minutes into injury time with another top quality finish, hammering the ball past Roche from an acute angle after being found by Mark Molesley.
Morecambe striker Lewis Alessandra missed an huge chance to open the scoring just before Cureton's first when he rounded keeper Artur Krysiak but then failed to find the target from six yards out.
The closest Morecambe came to a goal was when Ryan Williams saw a long-range free kick superbly tipped away by Krysiak.