The Portugal midfielder whipped in from the edge of the area as Nuno Espirito Santo's side matched their hosts at Old Trafford.
Wolves were lively in the first half and unlucky to go behind as Fred netted his first goal for United - the Brazilian firing in from just inside the box after Paul Pogba's excellent touch.
United, with former manager Sir Alex Ferguson watching on during his first visit to Old Trafford since having emergency brain surgery in May, were looking for a third straight league win.
The hosts were on top after the break, but Raul Jimenez's clever lay-off set up Moutinho for what was a deserved equaliser for the visitors.
The draw keeps Wolves one point b
The last time Wolves visited Manchester United in the Premier League, they fell to a 4-1 thrashing on their way to finishing bottom of the table. It was the same season Mourinho guided Real Madrid to a first La Liga title in four seasons.
Much has changed for both parties in the seven years since - Wolves dropping into League One before starting their ascent to the top flight and Mourinho making a title-winning return to former club Chelsea. But there was a sense of familiarity at Old Trafford as the well-acquainted Portuguese coaches took to either dugout.
Wolves boss Santo, Mourinho's back-up goalkeeper for Porto from 2002 to 2004, regards his former manager as "a big inspiration" in his career, but he more than matched his mentor tactically as Wolves' brand of quick, counter-attacking football caused the hosts problems.
Wolves were unlucky to head into half-time behind, with United goalkeeper David de Gea saving well from Willy Boly's header having earlier parried a smart turn and shot from Jimenez.
The Championship winners have benefited from an influx of Portuguese stars under the influence of agent Jorge Mendes, who acts as an advisor to Wolves' owners Fosun and also represents Mourinho.
And it was summer arrival Moutinho, with 113 Portugal caps to his name, who inspired the visitors' fight back alongside his younger compatriot Ruben Neves in midfield.
Moutinho's leveller was well deserved as Wolves became the first team this season to take points off both Manchester sides.
Fred on target as United's attacking stars struggle
Mourinho made a point of saying Alexis Sanchez, rested for the Champions League trip to Young Boys on Wednesday, would start in place of Anthony Martial on Saturday, with Marcus Rashford suspended.
The Chile forward was consistently Arsenal's best player before moving to Old Trafford in January, scoring almost a goal every other game in three and a half years with the Gunners. But he has struggled to replicate that form and is yet to find the net this season.
It was Sanchez's cross that was headed away in the build-up to the opening goal, but the 29-year-old was replaced just after the hour mark after being well marshalled by the Wolves defence, while striker Romelu Lukaku failed to have a shot on target.
United's attacking threat instead came from left-back Luke Shaw, midfielders Pogba and Fred and increasingly Marouane Fellaini, who saw a header saved by Wolves goalkeeper Rui Patricio.
Fred, a summer signing from Shakhtar Donetsk, took his goal well from Pogba's brilliant assist and also forced Patricio into a diving save from a free-kick.
The hosts increased the pressure late on and were improved by the arrival of Martial and Juan Mata, but looked vulnerable on the break and had De Gea to thank for keeping out an effort from Wolves substitute Adama Traore.
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