Wolves, elegant and fierce, advanced to the FA Cup semi-final for the first time in 21 years and Manchester United could do nothing to stop them. First Ole Gunnar Solskjær’s men were frustrated by their hosts, then they were taken apart. Goals from Raúl Jiménez and Diogo Jota confirmed Wolves’ superiority over their illustrious visitors.

Marcus Rashford’s strike in stoppage time changed nothing other than inconsequential statistics, halving Wolves’ margin of victory and doubling United’s tally of shots on target from a match in which they had a lot of the ball but were never in control. Wolves created the clearest opportunities and might have inflicted a truly embarrassing scoreline if not for some terrific saves by United’s goalkeeper Sergio Romero.

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Solskjær said this was United’s worst performance on his watch. “We lacked urgency and quality on the ball,” he said. He was right to add “but don’t take anything away from Wolves”, because Nuno Espírito Santo’s team were excellent. This was the latest in a series of fine displays that makes it hard to believe the men from Molineux were in the second tier this time last year.

“It’s down to talent based on organisation,” explained Nuno as if it were easy. Not only do his team stand seventh in the Premier League, with a semi-final at Wembley to come, they can realistically dream of winning a first major trophy since the 1980 League Cup. They are obviously not favourites for this competition – not with Manchester City around – but it would be folly to dismiss them.

United also wanted to win it. Nothing about their approach here suggested they took this tournament or their opponents lightly. Solskjær deployed his strongest available side, other than replacing David de Gea with Romero as per previous cup ties. He cast Jesse Lingard, Anthony Martial and Ander Herrera straight back into the starting lineup after recent injuries.

Nor was there anything to indicate that United’s confidence had been dented by last week’s reverse at Arsenal, their first domestic defeat under Solskjær. They made a good start, popping the ball about with promising intent. But Wolves are savvy operators and, though deprived of the ball for most of the opening quarter, they kept the visitors out of range. The home team’s goalkeeper, John Ruddy, did not have to make a save until the 13th minute. It amounted to little more than a warm-up, Rashford’s effort from long range never likely to reach the net.

Wolves were comfortable until the 26th minute when United opened them up with a cute one-touch move around the box before Lingard fizzed a low cross into the danger zone. Martial would have had a chance to score from six yards if not for an excellent tackle by Leander Dendoncker.

Wolves soon threatened at the other end, Romero having to make saves from Rúben Neves and Jota. In a taut contest any misstep could prove costly. Both teams had appeals for penalties turned down before the break, and then Chris Smalling got himself in trouble in midfield and Neves pierced the remains of United’s defence with a surgical pass from deep. Jota, however, was less precise, curling his shot too close to the advancing Romero, who batted it away.

Facebook Twitter Pinterest Raul Jiménez (right) celebrates his opener. Photograph: Sam Bagnall/AMA/Getty Images

Having contained United in the first half, Wolves grew bolder in the second. United began to flail. In the 53rd minute Jiménez, as strong as he is lithe and canny, held off Victor Lindelöf to connect with a corner by João Moutinho. The striker’s header from eight yards was en route to the net until Romero tipped it on to the crossbar.

Romero was forced into action again a few minutes later to push away a 20-yard shot from Moutinho. Now Wolves were seizing the upper hand. In midfield, Moutinho, Neves and Dendoncker started to flit between Nemanja Matic, Paul Pogba and Herrera like artful dodgers confronted by dull bouncers.

Solskjær needed to make a change but he did not react quickly enough. In the 70th minute Moutinho wriggled his way into the box and slipped a low pass through to Jiménez, who held off Lindelöf and Pogba before turning and firing low past Romero.

Now Solskjær replaced Herrera with Andreas Pereira. But Wolves scented blood and soon finished off their visitors. The killer blow came six minutes after the first. After clearing a corner Wolves overwhelmed United with a counterattack, Jota concluding it by outfighting and outwitting Luke Shaw before thrashing a shot into the net.

United’s woes deepened moments later when Lindelöf was dismissed for sliding through Jota to win the ball, but the referee downgraded the red card to a yellow after consultation with the video assistant referee. That was the only reprieve United got.

Wolves’ fans, meanwhile, hailed Nuno for guiding the club into an era that is reviving memories of their glorious past. “It means a lot,” said the manager. “As I walked by the stands there were people saying they saw the 1950s and 1960s and are still coming to the stadium. To see this joy as they leave the stadium – with a lot of beer, of course - is great.”