United would have moved up to third in the table, ahead of Arsenal and Tottenham, with victory at Molineux but Nuno Espirito Santo's side came from behind to win thanks to a Chris Smalling own goal.
Scott McTominay's first Manchester United goal put his side ahead but Diogo Jota, who scored as Wolves knocked Ole Gunnar Solskjaer's men out of the FA Cup last month, levelled.
Young's dismissal, the 100th of Mike Dean's Premier League career, came for a foul on Jota and in the 77th minute Smalling bundled the ball into his own net to ensure United have now lost three of their last four matches in all competitions.
United started rapidly and Jesse Lingard fired wide after just six seconds before Romelu Lukaku headed a brilliant Diogo Dalot cross straight at Rui Patricio.
They did lead in the 13th minute, however. Fred fed McTominay and the Scotlandmidfielder steadied himself before arrowing a skimming 25-yarder across Patricio and into the bottom-left corner.
It was Fred's first Premier League assist but Wolves equalised when the Brazilian lost possession, Raul Jimenez splitting the United defence with a clever throughball for Jota to finish well.
Leander Dendoncker fired over from six yards and Matt Doherty nodded Joao Moutinho's free-kick wide but Lukaku went close to restoring United's lead before half-time.
Patricio's excellent reflexes kept out McTominay's header in the 55th minute after Paul Pogba flicked on Lukaku's left-wing cross.
Referee Dean then reached his milestone by sending off Young, the United captain shown a second yellow card after catching Jota with a high challenge.
And although Wolves had failed to record an effort on the United goal since the interval, Moutinho's sensational cross caused chaos in David de Gea's box and Smalling nudged the ball home, the United goalkeeper's flimsy challenge not helping.
De Gea prevented Smalling scoring a second own goal and Wolves almost extended their lead in added time, substitute Ivan Cavaleiro holding off Victor Lindelof but rattling the woodwork.
Top-four race tightens up
Tottenham's lack of form has blown the race for Champions League qualification wide open, but United are failing to take advantage and losing momentum at a crucial point of the season.
There are only three points between Arsenal in third and Chelsea three places lower, with plenty of twists and turns to come in the run-in.
