Chris Hughton’s side came into the game having lost their last five in all competitions without scoring and facing a real fight to secure their top-flight status, with third-bottom Cardiff just two points behind them after their 2-0 midweek win at the Amex Stadium.
Wolves were still eyeing a seventh-placed finish in their first season back in the Premier League and they dominated the first half with Brighton struggling to get out of their own half.
The hosts continued to press after the break and rattled the woodwork but Albion held on for a draw to stop the rot and takes them three points clear of the drop zone with four games remaining.
Wolves boss Nuno Espirito Santo made two changes to his side following the 3-1 defeat at Southampton as Morgan Gibbs-White and Ryan Bennett replaced Romain Saiss and Leander Dendoncker.
For Brighton, Jose Izquierdo and Gaetan Bong returned to the starting line up as Alireza Jahanbakhsh and Bernardo dropped to the bench on the back of the Cardiff defeat.
Wolves made a bright start, with Brighton happy to try and keep things tight at the back, although the Seagulls were hit by the loss of Davy Propper to a possible hamstring injury after just 10 minutes.
The hosts continued to dominate possession as Brighton continued to sit back to frustrate their opponents, who continued to struggle to find a way through.
There was a hopeful penalty shout for Wolves on 23 minutes when Diogo Jota went down in the area under a challenge from Pascal Gross, but the Seagulls man got a slight touch on the ball when making his challenge.
The first real chance came on 33 minutes when a Gibbs-White flick-on picked out the run of Jota and he dragged a right-foot effort wide of Mat Ryan’s goal from the edge of the area.
Bruno then produced a fantastic last-ditch tackle to prevent Joao Moutinho a free run at goal and Bennett then headed a free-kick into the Seagulls’ area wide of the mark.
In first-half stoppage time, Ruben Neves’ long-range effort was deflected into the path of Jota and he watched as his strike hit the top of Ryan’s crossbar on its way out of play.
Matt Doherty had the first opportunity after the break when he got up to meet a Neves cross into the area on 51 minutes, but watched as Shane Duffy hacked his effort off the line.
There was very nearly an opener out of nowhere from the visitors moments later when Beram Kayal went for goal from 30 yards and his strike just cleared the top of Rui Patricio’s goal.
Brighton continued to be forced back in numbers as Jota went close on 73 minutes when he met Raul Jimenez’s cross and saw his header rebound off the post before substitute Dendoncker’s follow-up shot was saved by Ryan.
Two minutes later, Willy Boly got his head to a Doherty cross but couldn’t keep the ball down as it flew over Ryan’s crossbar. Dendoncker should have done better on 88 minutes when he guided a header straight into the hands of Ryan with the whole goal to aim at.