Albion's back-to-back home losses to Bournemouth and fellow struggler Cardiff City over the past week had left it in a perilous position.
Chris Hughton's men turned in a backs-to-the-wall performance at Wolves and are now without a goal in six matches, but they did avert a sixth consecutive defeat in all competitions, with Diogo Jota coming closest to a breakthrough for eighth-place Wolves when he headed against the post in the 73rd minute.
Brighton started nervously and suffered an early blow when influential midfielder Davy Propper sustained an apparent hamstring injury.
Jota engineered space amid a packed Brighton rearguard to pull a strike narrowly beyond the left post in the 33rd minute before the Portuguese forward miscued a volley against the top of the crossbar in first-half stoppage-time.
A mix-up between Willy Boly and Rui Patricio early in the second half almost saw the Wolves defender put through his own goal, and Propper's replacement Beram Kayal whistled a 25-yard strike just over as Albion began to show more ambition.
Wolves were struggling for their earlier fluency as the hour passed and Ryan Bennett's attempt from Joao Moutinho's corner was deflected behind.
Raul Jimenez fizzed a shot over on the half-volley before team-mate Morgan Gibbs-White inadvertently prevented him from converting a 71st-minute cross.
Jimenez turned provider for Jota to glance against the post and Brighton goalkeeper Ryan did brilliantly to deny substitute Leander Dendoncker on the rebound.
A wayward free header wasted by Boly suggested Brighton's near-permanent focus on defence was taking a toll, but they held on as Ryan again thwarted Dendoncker at close quarters.