Scott McTominay's first United goal, struck sweetly from the edge of the area, ensured that United would capitalise on a strong start under the lights at Molineux.
Solskjaer's visitors could have doubled their lead shortly after, when a flowing move presented Jesse Lingard with an unmarked header inside the six-yard box which was saved by Rui Patricio.
But Wolves gradually grew back into the game and equalised, taking advantage of Fred's poor touch to counter and score through Diogo Jota.
United were reduced to 10 men after the break when Ashley Young was shown red for a second bookable offence and, with an extra man, Wolves continued to dominate.
Their winner came from a United defensive mix-up, as a cross from the left went unclaimed and bounced in off Chris Smalling, with David de Gea left stranded.
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