A stunning Carlos Baleba strike from distance opened the scoring for Albion before Simon Adingra doubled the hosts’ lead with another fine goal from the edge of the area.
The Seagulls looked firmly in control of the game until Goncalo Guedes halved the deficit on the stroke of half-time after some poor defending.
Wolves, buoyed by that goal, were the shaper of the two teams after the break and nearly grabbed a quickfire equaliser. Jason Steele stayed alert to deny Rodrigo Gomes from close range.
Jack Hinselwood was the hero as he pulled out a miraculous goal-line clearance after Nelson Semedo’s cross was heading in via an Adam Webster deflection.
Wolves still threatened but Fabian Hurzeler’s substitutions proved crucial as Danny Welbeck burst clear and had a shot saved before Ferdi Kadioglu grabbed his first goal for the club on the rebound.
Perhaps thinking the game was won, Jason Steele gave the ball away cheaply in injury-time and Tommy Doyle fired in off the crossbar to give Wolves hope once again.
Albion just about got over the line, though, and secured progression to the next round of the Carabao Cup.
1.
Evan Ferguson of Brighton & Hove Albion celebrates scoring his team's second goal with teammates during the 2-2 draw against Wolves Photo: Mike Hewitt
2. Bart Verbruggen 6-10
One vital save from Larsen's header on 73 minutes but had little chance with either goal especially the deflected leveller. Photo: Matt McNulty
3. Joel Veltman 6-10
Another solid performance from the experienced defender. Playing some of the best football of his career under Hurzeler and disappointed not to take all three points Photo: Jack Thomas - WWFC
4. Jan Paul van Hecke 6-10
Great to to see the Netherlands defender back after his groin issue. A good defensive display and kept things nice and simple with his passing. Photo: Steve Bardens