United goalkeeper Sergio Romero, in for David de Gea, had kept United level with brilliant saves from Diogo Jota and Raul Jimenez either side of the interval, before the Mexican striker swivelled in the area to finally give Wolves the reward their domination merited with 20 minutes remaining.
Wolves were rampant and it was no surprise when the dangerous Jota doubled their lead six minutes later, shrugging off United's Luke Shaw on the break before shooting low past the exposed Romero.
United defender Victor Lindelof was shown a red card by referee Martin Atkinson for a touchline challenge on Jota, but it was downgraded it to yellow after a VAR review and, even though Marcus Rashford pulled one back very late on, Wolves - best of the rest in the Premier League - were worthy winners.
With Wembley on offer for the semi finalists, and having beaten Arsenal and Chelsea to get this far, the shot at FA Cup glory looked favourable and United had been tipped to go all the way as momentum built under Solskjaer. After this chastening defeat, fresh questions will be asked ahead of a two week domestic hiatus for the first international fixtures of 2019.
The first half was poor with the only noteworthy action an effort from distance by Rashford. Paul Pogba also tried his luck but Wolves, tentative up until then, began to grow into the tie. Joao Moutinho had a half chance, but Romero was then called into action for the first time as the Reds cup keeper saved superbly from the onrushing Jota when he came racing out to stifle the striker. Diogo Dalot appealed for a penalty after Jonny Otto appeared to handle, but referee Martin Atkinson instead gave a corner.
Romero's world class save from a Jimenez header underlined his status as the best stand in stopper in the English game. He came to United's rescue again moments later when he shovelled Moutinho's long-range strike over the top as Molineux sensed an imminent breakthrough.
As United struggled to find any rhythm, Nuno Espirito Santos’s side became increasingly confident. With the pressure increasing on the Reds, Jimenez came up with the opening goal. There were plenty of red shirts in the box but after initially blocking Jimenez, the striker was able to spin and squeeze in a finish on 70 minutes.
The Reds threw men forwards but, six minutes later, Wolves had moved further ahead to put the game beyond even Solskjaer's United. Jota burst clear one-on-one and outpaced Luke Shaw who slipped, and the Portuguese slammed in under Romero.
The nightmare almost became worse for United in the 81st minute as Wolves threatened to race away for a third. Goalscorer Jota sped down the right flank and Victor Lindelof stormed across to cover but slid dangerously into the rescuing tackle and floored the Wolves man.Referee Atkinson initially showed the Swede a red card but VAR overturned his decision, reducing the offence to a booking, and United remained with 10 men on the pitch, much to the fury of the Molineux crowd.
Juan Mata and Scott McTominay came on in a late bid by Solskjaer to find a late answer to the dire situation, adding to the earlier addition of Andreas Pereira.
United did snatch a consolation when Rashford turned to convert a cross by Shaw but a club noted for so many delirious and improbable comebacks had left it far too late to add to our catalogue of remarkable finales.
Overall team performance: 4/10
United Faithful Man of the Match: Sergio Romero