Town have enjoyed a recent upturn in form, their last defeat coming in the West Yorkshire derby against Leeds in September, but could not hold out against Sami Hyypia’s struggling side.
Jacob Butterfield gave the hosts an early lead, but Seagulls defender Lewis Dunk levelled shortly before the break.
Brighton finished the game with 10 men following Kazenga Lua Lua’s injury-time red card.
Terriers boss Chris Powell opted to name an unchanged line-up following Saturday’s 4-2 home win over Blackpool.
Opposite number Hyypia made just two changes to the side beaten by Middlesbrough last time out, Adam Chicksen and Chris O’Grady replacing injured duo Joe Bennett and Joao Carlos Teixeira.
Town got off to an ideal start when they took the lead after just 10 minutes.
Sean Scannell showed some neat touches down the right before playing in Tommy Smith to pick out Butterfield, who lashed the ball home from close range with a little help from the underside of the bar.
The visitors appeared to be struggling for inspiration in attack as a frustrated looking Sam Baldock twice opted to shoot from range with little or no support arriving.
But the Seagulls did manage to pull themselves level on 38 minutes.
Dunk thumped home his fifth goal of the season, again with a touch off the woodwork, after the Huddersfield defence failed to clear Jake Forster-Caskey’s initial corner.
Harry Bunn ensured Town ended the first half on the up, his fizzing effort pushed away by David Stockdale after the attacker had done well to cut inside.
And Stockdale had to be alert again soon after the restart, this time getting two strong fists to Jack Robinson’s shot as the hosts went in search of a second goal.
Wigan loanee Grant Holt came close to adding it just after the hour mark. He was well placed to meet Butterfield’s cross with a firm volley, but again Stockdale did well to keep it out.
But, in their only attack of the second half, Brighton looked to have snatched all three points with just minutes remaining.
Forster-Caskey fed Baldock to slot home a cool finish, but the assistant referee’s flag had already been raised for offside.
Lua Lua’s injury-time dismissal for a second bookable offence summed up another frustrating evening for Hyypia’s side, who remained without a league win in their last nine outing.