Brighton clicked into gear in the 20th minute when Andrea Orlandi raided down the flank and lifted a cross into the area, where Jose Ulloa was able to head into the net.
Orlandi nearly doubled his side's lead when he coasted into the penalty area unmarked but he wasn't able to beat Alex Smithies in the Terriers goal.
Just before half time Huddersfield equalised through James Vaughan, whose overhead kick flew into the net after the ball had bounced around the penalty area following Sean Scannell's cross.
Ashley Barnes missed a gilt-edged chance after the break as he latched onto a ball into the area but he lost his composure when unmarked and headed over.
Brighton finally got their goal as Ulloa headed home from a corner and seconds after the restart he latched onto a short back-pass and rounded Smithies to complete his hat-trick.
Gus Poyet's side made it four from the penalty spot when Craig Mackail-Smith was felled by Paul Dixon, and David Lopez made no mistake firing the ball home to secure the win.