Northampton dominated the first half-hour with some neat approach work which was not matched by their finishing.
Long-range efforts from Jackman and Luke Guttridge failed to seriously trouble Matt Murray in the Hereford goal. Leon Constantine was also off target when he got his head to a Jackman free-kick.
Hereford's attack finally got moving and Lionel Ainsworth, on his loan return from Watford, volleyed over the bar from 30 yards.
The Bulls' best efforts came from Steve Guinan who forced a couple of saves from keeper Frank Fielding with shots set up by Richard Jackson and Ben Smith.
But the half's best chance fell to Constantine, three minutes before the break. The tall forward rushed a clear chance and sent the ball wide as Murray raced off his line to challenge.
Three minutes into the second period, Northampton took the lead when Jackman demonstrated his expertise from dead-ball situations.
The midfielder curled a left-foot shot around the Hereford wall from 25 yards and the ball beat Murray's despairing dive before nestling in the corner of the net.
The Cobblers' second goal, 13 minutes later, owed a little to good fortune. Jackson, in attempting to clear a throw-in from Scott McGleish, drove the ball against Bulls skipper Karl Broadhurst's head.
The rebound could have gone anywhere but fell at the feet of Gilligan who slipped a shot between Murray's legs and into the net.
Hereford used all of their three substitutes, bringing on forward players in an attempt to claw their way back.
But, although Andy Williams had a header well saved by Fielding, the visitors held on comfortably to leave Edgar Street with the three points.