A first half goal from Liam Davis gave the Cobblers the lead at the break.
Leeds pressure paid off and Jermaine Beckford levelled in the 69th minute. Prior to that the visitors had hit the post and the crossbar and after their goal continued to press for a winner.
But it was Bignall who stole the show when he rose to head home Danny Jackman's corner in the 87th minute.
That's back to back wins now for Northampton who face Colchester this coming Saturday in the re-arranged fixture.