Jonas Lossl’s own goal gifted the Seagulls a lead that lasted just two first-half minutes, before Shane Duffy’s loose pass returned the compliment to let Steve Mounie equalise.
Davy Propper spurned Brighton’s first gilt-edged opening with just a minute on the clock, and then saw red in the final quarter for a studs-up tackle on Jonathan Hogg.
Chris Hughton’s Brighton slipped to a fourth game without a win, with one nervy eye always trained on a season-ending run of facing Manchester United, Manchester City and Liverpool in just nine days.
Mounie ended Huddersfield’s Premier League goal drought on 427 minutes, the Benin striker netting for the seventh time in the league this term.
The Terriers’ own winless streak extended to five games, but manager David Wagner must have been reasonably satisfied with just a second league point since the 2-1 win at West Brom February 24.
“Our promotion last season was a fairytale; this season, if we survive, for me, this is another level,” said Wagner.
“This would be a miracle, and the players are five games away from completing this miracle.
“These players, we have all together represented Huddersfield Town as a football club in the Premier League, where we compete against multi-billionaires and against countries.
“I’m so happy that we still have the chance to make this miracle happen.”
Propper ought to have handed Brighton the perfect start, but instead of blasting home he fired wide with just Lossl to beat.
The Holland midfielder’s glaring miss stunned the hosts for some 10 minutes, until they left another fine opening unconverted.
This time it was Jose Izquierdo who should have done better when through on goal, with Lossl just beating him to Glenn Murray’s slide-rule pass.
Lossl’s earlier heroics counted for nought when his clanger gifted Brighton the opener.
The Denmark stopper should have dealt comfortably with Solly March’s regulation 20-yard drive, but instead palmed the low effort onto the post - with the rebound cannoning off his body and over the line.
No sooner were Brighton ahead however, than another error let the Terriers draw level. Duffy’s miscued back pass left Mathew Ryan in no man’s land and only able to watch on as Mounie rounded him and poked into the empty net.
Huddersfield’s seven-hour Premier League goal drought was over, and palpable relief flowed immediately through the visitors.
Brighton dominated from the off after the break, but could find no end product as their jittery build-up play continued.
Lewis Dunk nodded wide when he should have scored from March’s free-kick, Dale Stephens saw his rising effort tipped over the bar and Duffy had a header easily cleared.
That studs-up sliding tackle on Hogg then ended Propper’s afternoon prematurely, courtesy of a red card that was perhaps necessary, but definitely harsh.
Hughton’s immediate reaction was to sacrifice one of his few creative outlets Pascal Gross, with Beram Kayal tasked to add stability but also whatever possible impetus.
Izquierdo still had time to fluff another cast-iron opening, the Colombia forward latching onto Leonardo Ulloa’s through-ball, only to choke in front of goal and let Lossl take control.