The Seagulls dominated possession throughout the lively contest, but they ultimately lacked a cutting edge in the final third and were forced to play out their second successive 0-0 draw in the Premier League.
Wolves, meanwhile, spurned a number of decent opportunities to break the deadlock, particularly in the second half, but their resolute defending admirably thwarted a Brighton outfit lacking ideas in attack, and Gary O'Neil's side can head home the happier of the two teams despite claiming only a point for their troubles.
A draw for Roberto De Zerbi's men has helped extended their unbeaten home run to nine matches, and they have also moved above Manchester United into seventh place in the Premier League table on goal difference.
As for Wolves, their three-game winning streak in the top flight has come to an end and they remain 11th in the table, level on points with Newcastle United in 10th and only three points adrift of Brighton in seventh.
Brighton started on the front foot and looked lively in possession, with Billy Gilmour distracting the play in the opening exchanges from the middle of the pitch.
The first real chance of the contest was presented to the Seagulls in the 12th minute, when an inviting corner kick from Pervis Estupinan was flicked on towards Facundo Buonanotte at the back post, but his stooped diving header, which lacked power, was cleared off the line by Tommy Doyle.
Brighton had 69.6% possession inside the first 15 minutes of the match, but Wolves posed a threat on the counter-attack and came close to opening the scoring when Pedro Neto, starting his first league game since October, burst towards the Seagulls penalty area and fizzed a left-footed strike from around 25 yards out narrowly wide.
At the other end, Jose Sa was left puzzled by a dangerous free kick whipped into the six-yard area by Pascal Gross, and the Wolves goalkeeper was fortunate to divert the ball over his crossbar.
Tempers flared slightly towards the end of the half following an initial coming-together between Craig Dawson and Gilmour, with O'Neil acted as peacemaker on the touchline to separate De Zerbi and Wolves coach Neil Cutler, who was booked for his involvement.
Matheus Cunha then received a harsh yellow card following a minor collision with Gilmour, much to the frustration of the Wolves attacker who has to be dragged away by his teammates to avoid receiving a needless second booking for dissent.
Wolves came out of the blocks with intent after the break and Cunha was presented with two huge chances less than 30 seconds after the restart, firstly poking a low shot straight at Jason Steele following a promising team move from the visitors, before firing the rebound high over the crossbar.
Brighton responded well, but Wolves defender Nelson Semedo did brilliantly to block a shot from Joao Pedro before Jack Hinshelwood's low cross was intercepted and deflected onto the near post by Max Kilman.
Wolves continued to offer a threat on the break and came forward with purpose just before the hour mark, with Neto forcing Steele into making a save at his near post before Dawson blazed a volley over from the resulting corner.
Brighton switched to a back three in the final 20 minutes and pushed an extra body forward in search of an opener, but that tactical tweak seemed to benefit Wolves who looked the most likley to break the deadlock.
Neto, the visitors' most dangerous player down the right flank, burst in behind and fizzed a low delivery across the six-yard box that was crying out for a Wolves player to tap home from close range, before Cunha lacked composure and wasted a decent opportunity when he fired a shot behind after rounding Steele, who had rushed around 30 yards off his line.
Cunha then released Mario Lemina who broke from midfield to race through on goal, but his powerful strike from a tight angle on the right channel was well saved by Steele.
Both sides eventually had to settle for a point, and they will now shift their focus back to the FA Cup, with Brighton taking on Sheffield United at Bramhall Lane on Saturday, and Wolves locking horns with West Midlands rivals West Bromwich Albion at The Hawthorns on Sunday.