The home side dominated the second half without getting the breaks and have yet to win a home league game under boss Gus Poyet.
Midfielder Anthony Pilkington went close for the Terriers in each half and nearly snatched victory when his tremendous 40-yard free-kick cannoned back off the crossbar 11 minutes from time.
Goalkeeper Alex Smithies crucially tipped over his own bar from team-mate Peter Clarke as Lee Clark's men held on.
Pilkington should have hit the target 10 minutes before the break when, goalside of his marker, he put the ball over from a Danny Drinkwater free-kick.
French winger Seb Carole blazed a late chance over for Brighton, who have not won at home in the league for four months.