Cheltenham Town struck in the first 40 seconds and the last to claim victory at Highbury.
Troy Brown headed home from a Matt Richards corner with just 38 seconds gone to give the visitors the lead, one they could easily have extendedthrough Byron Harrison before Fleetwood had managed a shot.
Shell-shocked Town did get a chance to level before the break, Daniel Carr’s header kept out by keeper Scott Brown.
Carr had another chance after the break, Brown again thwarting Fleetwood.
The keeper was having an inspired day, keeping out Jon Parkin before the Robins added a second on the break.
Harrison charged forward, picking out the run of Jermain McGlashan, the Cheltenham man passing Ryan Cresswell and rounding Scott Davies to make it a misereable end for Fleetwood.