What would Wolves fans have given you last August for an FA Cup ­quarter‑final home derby against Championship opposition and a place secure in the top half of the Premier League? A strange look, probably.

Yet Gary O’Neil’s first six months in charge have led not to a battle against relegation but renewed optimism that the unity and upward ­momentum of Nuno Espírito Santo’s reign is returning.

Related: Casemiro’s late nod topples Forest as Manchester United roll on in FA Cup

Mario Lemina, who epitomises the heart and soul that is echoing around Molineux, scored the winning goal within two minutes as Brighton’s extreme injury problems meant their 72% possession counted for nothing. They will just have to put up with aiming to win the Europa League instead.

Their goalkeeper Jason Steele, up for a corner as the clock ticked into the 96th minute, had Brighton’s best chance when Lewis Dunk’s header fell his way. But he grabbed at the opening, unsurprisingly, and mis‑hit it wide from three yards out.

Wolves’ fourth successive win was not beautiful but, as against Sheffield United on Sunday, a single goal was enough to see them over the line.

O’Neil, appointed on the eve of the Premier League season, will not dampen Wolves fans dreaming of a Wembley semi-final place as they secured a home tie with Coventry. “I’m sure the fans will be dreaming about Wembley,” he said, “and I’ll be planning how to beat Coventry.

“Coventry are a good side I’ve seen quite a lot of in the Championship and we’ll be expected to roll them by ­everyone apart from our ­dressing room. People just assume we’ll beat them. If we’re even at 95%, it won’t be enough.”

Brighton were without nine ­players, though Roberto De Zerbi said Evan Ferguson, Joel Veltman and Tariq Lamptey could be back for the game at Fulham on Saturday. They looked a shadow of the team that won 4-1 here in O’Neil’s first game in charge at Molineux but De Zerbi was pleased with how his young makeshift team performed. “The future of Brighton was on the pitch today,” he said. “Maybe not ready to play at this level, in this competition, but we’re doing well to match last season despite a lot a lot of problems.”

Wolves, notwithstanding their need to keep Pedro Neto and Pablo Sarabia back for the first hour, made the best possible start.

Jean-Ricner Bellegarde, filling in up front, spun away from Jan Paul van Hecke to make quick strides down the left channel. When his cross was spilled by Jason Steele, Lemina was quicker to the loose ball than ­Pervis Estupiñán and, from his seat on the ground, scythed home his fifth goal of the season.

Brighton, winners here on their three previous visits, proceeded to dominate the rest of the game. Their centre-halves, Igor Julio and Van Hecke, frequently joined the attacks as Wolves were pinned back. But from their best first-half chance Facundo Buonanotte headed wide Estupiñán’s left-wing cross.

Indeed Wolves could have gone further ahead but Santiago Bueno misdirected Tommy Doyle’s free‑kick when offered a clear sight of goal. Then when Julio under-clubbed his back‑pass, Steele had to produce a clanking tackle to prevent Bellegarde stealing in.

Brighton upped the ante by ­bringing on Danny Welbeck, and switching to a back four but, although they continued to dominate even after Neto and Sarabia came on, Wolves did look far more dangerous on the break. On several occasions Neto was a delayed pass or a defensive recovery away from breaking clear for the chance of a second goal.

Hwang Hee-chan went down with what O’Neil described as a minor hamstring injury that will most likely rule him out of the trip to Newcastle. “I’ll be amazed if he plays ­Saturday,” the Wolves head coach said. “At least I can have another couple of days ­playing ‘Who plays No 9’ on my white board.”

Brighton, with their appetising Europa League last-16 first leg at Roma next Thursday, tried to manage their energy levels by using all five substitutes and keeping the ball as much as possible. Sure as hell beats chasing it.

The Molineux crowd understood the game: Brighton could have the ball if they could have the quarter-final place. “Gary O’Neill’s barmy army” rang around the ground for the final stages even as Brighton pressed for the equaliser.