Daniel East was sent off for the visitors after 29 minutes, earning himself a second yellow card for his challenge on Fleetwood's Jamie McGuire.
The hosts had the ball in the net twice in the first half, both times from McGurie headers ruled out for offside.
Junior Brown looked to have snatched it for the Cod Army late on but his strike was ruled out, the linesman insisting the winger had taken he ball out of play before squeezing it past Lee Nicholls in the Cobblers goal.
Fleetwood had claims for a penalty late on when Kelvin Langmead was judged to have handled Damien Johnson's shot, referee Steve Rushton deciding the offence had taken place outside of the box - Mangan blasting the free kick straight at Nicholls.
But Mangan was on target in the second minute of injury time heading home at the back post to extend a purple patch for Micky Mellon.