Antony Kay got the ball rolling after 21 minutes when he headed home Anthony Pilkington's right-wing cross.
Liam Dickinson, who enjoyed a successful loan spell with Town last season, brought Brighton level in the 34th-minute. The Derby striker expertly picked out the top corner from the edge of the area. But parity lasted just 60 seconds before Huddersfield broke from the kick-off and Peter Clarke turned the ball home from close-range.
The hosts extended their lead just before the break from the penalty spot when Lee Novak was flattened inside the box by Albion keeper Michel Kuipers, who was shown a red card for the challenge. After a long delay while Kuipers left the field, Novak held his nerve to coolly slot the ball past substitute keeper Graeme Smith.
Jordan Rhodes was unable to add to his goal tally for the season after he was brought down for another penalty by Andrew Whing as Smith tipped his 54th-minute spot-kick round the post. Rhodes made amends by setting up Gary Roberts' goal 10 minutes later as the floodgates opened.
Daniel Drinkwater found the bottom corner from the edge of the box in the 69th minute before setting up Theo Robinson to make it 6-1 four minutes later and Robinson completed the rout in injury time with a tidy finish from 12 yards.