Tom Fraser netted the Seagulls' opening goal in the ninth minute at Edgar Street on Tuesday night to end their goal famine of six hours and 10 minutes without a goal.
Striker Lloyd Owusu headed the ball down to Fraser who beat goalkeeper Peter Gulacsi with an overhead kick from eight-yards.
The Seagulls continued to dominate the first-half with Craig Davies and Tommy Elphick going close to increasing their scoreline.
Goalkeeper Michel Kuipers smothered the ball at the feet of Hereford's leading marksman Steve Guinan as the Bulls tried to get back into contention after the break before Brighton clinched their victory in the 75th minute when Owusu beat Gulacsi with a low shot from 15-yards.
Kris Taylor scored a consolation goal for Hereford in injury time after Kuipers had saved a Guinan penalty, given for a foul by Adam Virgo on Febian Brandy.
Brighton remain 22nd but are now only five points behind 20th-placed Crewe and they also have a game in hand. The Bulls are six points back in 23rd.