Brighton made the most of early gifts from careless Wolves to reach the fourth round.
But Albion boss Fabian Hurzeler was made to sweat after they flirted with throwing away a two-goal lead in an uncomfortable second half before Ferdi Kadioglu came off the bench to score what turned out to be the decider.
"We didn't manage the game like we should, we didn't control it in some situations," he said. "There are a lot of things to improve."
Wolves’ second string were desperately sloppy and at times looked disinterested in a dismal opening half. Yet they were greatly improved after the break, spurned two great chances to make it 2-2 and were still alive in added time when Tommy Doyle made it 3-2.
“We didn’t do as well as we should have in the first half,” manager Gary O’Neil said. “We fixed a few mistakes at half-time.”
But those errors proved decisive.
Carlos Baleba’s opener was beautifully finished - a curling effort into the bottom left corner from more than 20 yards.
Yet it only happened because Joao Gomes dawdled, unaware that Albion’s midfielder was on his shoulder waiting to steal the ball.
Brighton’s second arrived thanks to another long-range attempt from Simon Adingra, who was casually permitted to cut in from the left with neither tepid Pedro Lima nor Santiago Bueno doing much to close him down.
Still, for all their folly, Wolves went into the break only a goal behind after Matt Doherty charged forward and pulled a pass back for Goncalo Guedes to drill home.
Wolves resumed much brighter and Brighton were grateful to see Jack Hinshelwood produce a fine goal-line clearance while Guedes scuffed wide.
But Albion looked safely through when Danny Welbeck’s effort was parried by Sa for Kadioglu to tap in. Doyle’s strike led to a mildly nervy ending.
“We played very well for 44 minutes, we then made silly mistakes,” said Hurzeler, who is yet to taste defeat. “We weren’t clean and clear.”