Former manager Alex Ferguson was back at Old Trafford for the first time since his May health scare, but United failed to put on much of a show for him, instead producing a performance which surely would have resulted in the Scot's infamous "hairdryer" treatment.
Although United looked particularly off the pace early on and rode their luck, they broke the deadlock in the 18th minute, with Fred getting his first goal for the club.
Joao Moutinho scored Wolves' deserved equaliser with a fine finish early in the second half and, although United upped the pressure late on, they could not find a winner in 'Fergie time', as they slumped to another disappointing result.
Wolves looked vastly superior to their hosts in the early exchanges and forced David de Gea into two smart saves, as Raul Jimenez and Willy Boly threatened.
But United made the most of those let-offs and took the lead against the run of play 18 minutes in – Fred finding the bottom-left corner from 20 yards after Paul Pogba's clever disguised pass.
The Brazilian nearly got a second on the stroke of half-time, but his fine free-kick was tipped on to the post by Rui Patricio.
Wolves deservedly restored parity just after the interval, however, as Jimenez teed up Moutinho on the edge of the box and the midfielder found the top-left corner.
United huffed and puffed towards the end, with substitute Juan Mata offering a little more creativity than Alexis Sanchez, but Wolves held on, Nuno Espirito Santo successfully frustrating his "inspiration" Jose Mourinho.
What it means: Lukaku's supporting cast lacking craft
Romelu Lukaku endured a difficult outing on Saturday, with the supply to him generally poor.
Pogba looked the most likely to create chances for him, but otherwise United's attacking players were disappointing, with Sanchez and Jesse Lingard particularly ineffective.
But, to be fair to Sanchez and Lingard, neither would consider themselves to be natural wingers, yet Mourinho persists with them on the flanks.
Selfless Jimenez leads from the front
He may not have got on the scoresheet, but Jimenez made a real impact in attack for the visitors. His hold-up play was excellent, as shown when setting up Moutinho, he dropped deep to good effect and even his runs in behind troubled United. His former Benfica colleague Victor Lindelof had a difficult day.
Sanchez produces little spark once again
United's Chile forward certainly cannot be accused of not trying but his passing was sloppy and he made little impact in the final third. You have to wonder how long Mourinho will continue to play him out wide.
Key Opta Facts
6 - Man Utd have dropped six points from seven Premier League games at Old Trafford against newly-promoted opposition under Jose Mourinho; more than the Red Devils had dropped in 10 seasons in the top-flight between 2006-07 and 2015-16 (5 pts). Glum. pic.twitter.com/LdIogg0eRP— OptaJoe (@OptaJoe) September 22, 2018
- Wolves have avoided defeat at Old Trafford against Man Utd in all competitions for the first time since November 1980, stopping a run of eight successive losses.
- Fred is the 500th different player to score a competitive goal for Man Utd (excluding own goals).
- Paul Pogba has been directly involved in six goals in his seven starts in all competitions for Man Utd this season (4 goals, 2 assists).
After an EFL Cup date with Frank Lampard's Derby County on Tuesday, United's next Premier League outing sees them travel to West Ham. Wolves host Leicester City in the cup, before then welcoming Southampton to Molineux in the league.