Goals from Simpson on 28 minutes and Bartley on 89 allowed the League One side to progress to the next stage of the Johnstone's Paint Trophy and it was a deserved victory as they dominated for large parts of the game.
The Cobblers were handed a boost however by the return to action of top scorer Marc Richards who appeared as a 56th minute substitute.
He will now come into contention for a starting place as Chris Wilder's side return to league action at Cambridge United on Friday night.