Spanish defender Bruno Saltor raised hopes of a fourth successive home win for the Seagulls with a 70th-minute opener.
But Wolves hit back to equalise four minutes later when Rajiv Van La Parra’s cross went in off keeper David Stockdale.
Kenny Jackett’s men pressed strongly for a late winner and nearly clinched all three points when a low shot from Bakary Sako was pushed onto the post by Stockdale.
Wolves keeper Tomasz Kuszczak, released by Brighton last summer after helping them to the Championship play-offs in successive seasons, was called into action after only two minutes.
The 32-year-old Pole saved a goal-bound header from recalled striker Craig Mackail-Smith following a teasing cross into the edge of the six-yard box by Beram Kayal.
Brighton were fortunate to escape after eight minutes following a defensive mistake by Lewis Dunk, who gave the ball away under pressure from Van La Parra.
Benik Afobe went through on goal and had a shot well saved by keeper Stockdale before leading scorer Sako picked up the rebound and saw his low drive cleared off the line by skipper Gordon Greer.
The Seagulls should have broken the deadlock when Mackail-Smith shot wastefully wide from eight yards after a sloppy back-pass from Sako.
Brighton’s former Charlton midfielder Dale Stephens, called up for his first start in 11 months, was off target from close range after a free-kick from Danny Holla was flicked on by Greer.
Albion keeper Stockdale kept his side on terms by pushing a low left-footed shot from Afobe around the post after Kortney Hause had fed the striker.
Wolves, playing at the Amex Stadium for the first time since they were relegated from the Championship two seasons ago, threatened when Sako had a goal-bound shot saved by Stockdale before midfielder Kevin McDonald shot wide.
Albion captain Greer did not stand on ceremony by clearing a dangerous ball into the box by James Henry over the bar as Wolves attempted to step up their game after the interval.
The match was finely poised when striker Mackail-Smith failed to hit the target with a curling effort having been set up inside the box by Portuguese midfielder Joao Teixeira.
Mackail-Smith had the ball in the net on 59 minutes after Kuszczak parried a low shot from Teixeira, but referee Trevor Kettle ruled that the striker, a yard from goal, was in an offside position.
Patient build-up play involving Stephens and Bruno Saltor set Teixeira up with an opportunity in front of goal, but the Liverpool loanee snatched at the chance and blazed over with only Kuszczak to beat.
Albion broke the deadlock with 20 minutes remaining through Spanish defender Bruno who drilled a low shot under the body of Kuszczak after Inigo Calderon had an effort parried.
But Wolves hit back to level in the 74th minute when van La Parra broke down the right, getting the better of Joe Bennett, and his cross to the near post was palmed into his own net by Stockdale.
It was a particularly disappointing way for Brighton to concede the lead as former Fulham keeper Stockdale was left exposed at his near post as the spoils were shared.