The Seagulls took the lead on 29 minutes after Solly Marchs left-footed shot hit the post and trickled over the line via Jonas Lossls arm.
But Huddersfield responded immediately, courtesy of a woeful attempted back-pass from Shane Duffy, with Steve Mounie making no mistake to compound the error with a cool finish having rounded Mat Ryan.
Davy Propper was shown a straight red card following a late challenge on Jonathan Hogg (74), and both teams had their opportunities to go on and seal all three points in the second half, but there remains a three-point gap between them in the fight for Premier League survival.
Brighton, who stay 13th, nearly made the perfect start as Propper latched onto Ezequiel Schelottos long ball over the top to breach the Terriers defence but the Dutchman - still awaiting his first Brighton goal - fired wide.
Huddersfield - who remain 16th - responded as Mounie warmed the gloves of Ryan having been set-up by Terrence Kongolo, before Lossl got down smartly at the feet of Jose Izquierdo during a blistering opening 15 minutes.
Brighton made the breakthrough as March took aim 25 yards out, with his shot rolling a yard over the line after the ball had ricocheted off a post and the outstretched arm of Lossl.
But a lapse of concentration from Shane Duffy down the other end allowed Mounie to end Huddersfields goal drought - which stood at 427 minutes - meaning it was all square at the interval.
Brighton had the first good chance of the second half as Lewis Dunk rose to meet Marchs inviting free-kick, but the defender could only direct his header wide. Lossl then produced a superb save to deny Dale Stephens but Huddersfield were handed a numerical advantage with 16 minutes remaining.
Propper dived into a 50-50 challenge with Hogg but led with his studs, leaving referee Anthony Taylor with little choice but to show a red card. Despite the dismissal, it was Brighton who came closest to finding a winner with Lossl rushing out to deny Izquierdo as the points were shared.
