Having been on the wrong end of a 5-2 defeat eight days ago, Northampton were keen to put on a much-improved display and did so right from the start.
On-loan Derby defender Andy Todd impressive on his debut and the Cobblers restricted Leeds to create the best chances early on, with Scott McGleish heading wide from a good position and Ryan Gilligan smacking the post from 20 yards.
However Cobblers deservedly took a 28th-minute lead when Liam Davis beat Lucas with a superb shot from the edge of the box.
Jermaine Beckford twice went close to an equaliser as Leeds then dominated the second half and after Andy Robinson had been denied by Fielding and Luciano Becchio hit the crossbar, they drew level in the 69th minute when Beckford headed home at the far post.
But Northampton won it in the 87th minute when Bignall headed home Danny Jackman's corner.