The Cobblers scored three goals in four minutes, the first coming just seven minutes from time, to come from two goals down against Northwich Victoria.
The non-league side had been dreaming of a tie against one of the Premier League big guns when goals from Ball and Bennett looked to have won them the tie.
But strikes from Hoskins, Taylor and Calvert-Lewin ensured a £27,000 bonus for Town from the FA prize fund and all eyes on Monday's draw, which takes place at 7pm and will be televised live on BBC2.
To cap the strangest of days at Sixfields, the game took place against the backdrop of a serious fire at the Sixfields pub, a popular pre-match haunt for many supporters.