Defender Jamie McCombe headed in his fifth goal of the season as he pounced when Joey Gudjonsson's shot was deflected into the air and he sent a looping header over goalkeeper Casper Ankergren and into the net seven minutes from time.
Brighton striker Glenn Murray had made up for a first half penalty miss by toe-poking the visitors in front after 54 minutes.
The lead lasted barely two minutes as Huddersfield's Jordan Rhodes scored his fourth goal in three games with a powerful header from a Gary Roberts free-kick. Murray missed a penalty after he was brought down by Town skipper Peter Clarke, who was lucky to be shown only a yellow card for a late lunge.
Brighton, who have now failed to win in four league matches, went closest before the goals went in when Chris Wood hit the outside of the post from a tight angle after being put through by Elliott Bennett after 51 minutes .
The game was summed up after the final whistle by ugly scenes as both sets of players squared up to each other. Staff from both clubs had to separate the players.