The point for the Seagulls ended a run of three successive defeats, but their goal drought continues and they are now without a goal from one of their own players for nine hours and 20 minutes.
Albion are still not out of danger towards the bottom of the table and are seven points above the drop zone with three games left.
Huddersfield, with only one defeat in their previous six games, recalled striker Ishmael Miller and he put an angled shot over early on after a strong run into the area.
On-loan Manchester United left-back Reece James headed away a dangerous cross from Mustapha Carayol before Terriers keeper Alex Smithies claimed a header by Leon Best following a cross by skipper Inigo Calderon.
Huddersfield had a let off in the 15th minute when, after a corner by Dale Stephens, Lewis Dunk misdirected his header and Greg Halford put a close-range shot into the side netting.
The Terriers had the chance to break the deadlock when Miller found him eight yards from goal, but his right-footed shot was palmed away by Albion’s former Fulham keeper David Stockdale.
Midfielder Carayol, on loan from Middlesbrough, came close to hitting his first goal for Brighton when he put a shot against the crossbar after Bruno Saltor whipped in a fine ball to the far post.
Miller then went close at the other end with a toe poke which went just wide of the far post after getting the better of Dunk and Beram Kayal.
Albion looked the better side on the ball in the first half and Liverpool loanee Joao Teixeira was off target after a strong run shortly before the break.
The Seagulls, with only one win from their previous seven games, threatened soon after the interval through Kayal, who fired wide from a short pass by Leon Best.
Carayol had the chance to threaten inside the area but overran the ball and Huddersfield keeper Alex Smithies was able to make a comfortable save.
The Seagulls withdrew Carayol in favour of Kazenga LuaLua as manager Chris Hughton attempted to pep up his misfiring front line just short of the hour mark.
Dunk should have hit the target for the Seagulls when he headed a Stephens corner over before Hughton introduced striker Craig Mackail-Smith in place of Best.
Portuguese midfielder Teixeira had to be stretchered off late on for the Seagulls following a challenge with Wells for which the Brighton man was booked.
Teixeira was carried off with his right leg strapped up and he was replaced by Chris O’Grady.
Albion lived dangerously as both Jacob Butterfield and Wells were denied by the frame of the goal in a Huddersfield raid in the closing stages.