Raphael Varane scored his third goal for Manchester United
Erik ten Hag's side hardly created a chance of note until Bruno Fernandes found Aaron Wan-Bissaka with a superb pass inside the area.
The right-back calmly lifted the bouncing ball to the edge of the six-yard box, where Varane used his height to get above Nelson Semedo and head home.
It was extremely harsh on Wolves, who made light of last week's change of manager to produce a superb performance in Gary O'Neil's first game in charge.
O'Neil was booked for his protests in claiming for a late penalty as United clung on for a fortunate victory.
United's debutant goalkeeper Andre Onana avoided punishment in added time for clattering into Sasa Kalajdzic when he came for a cross without making contact with the ball.
Matheus Cunha should have given Wolves the lead before then as Pablo Sarabia's low cross found him unmarked just beyond the far post but despite steadying himself, the Brazilian hit the outside of the upright.
Cunha fizzed a low shot wide just before the break and Pedro Neto fired straight at Onana before Varane's decisive effort while Fabio Silva had two goal-bound efforts saved as Wolves pressed for an equaliser.
In the build-up to the game US broadcaster NBC was given a pitchside interview with Sir Alex Ferguson.
The legendary United boss praised the work Ten Hag is doing and said the situation for his old club would improve markedly once £72m forward Rasmus Hojlund has recovered from the back injury he arrived from Atalanta with.
Not long afterwards, Hojlund took his seat alongside Tom Heaton and Jonny Evans at the back of the directors' box.
Sir Alex's words were given added credence when the game started as Marcus Rashford failed to make any impact as the main striker and Alejandro Garnacho and Antony were equally muted on the flanks.
Perhaps it should not have been a surprise given in 11 meetings over the past four years only twice have these two sides managed to produce more than a single goal between them.
Wolves fans will feel they should have been awarded a late penalty
United's other new outfield recruit Mason Mount also failed to make an impact and in a game where so much of their offensive play was average, Fernandes' inspired pass to create the goal stood out.
The Old Trafford crowd do have a new hero in Onana though. The Cameroon keeper produced a conservative performance with the ball at his feet and did not venture too far from his goal when the home side pressed forward.
However, the saves he made were important and the reception the former Ajax and Inter Milan man received from the stands indicated the home fans are very much on his side.
That O'Neil spent the immediate seconds after the final whistle still unable to comprehend that his side were denied a penalty and the Wolves fans bellowed their support for their new manager and his team said everything about how the visitors played.
O'Neil made a point of saying before the game that "clubs normally get six weeks" to prepare for their opening game. The former Bournemouth boss got four days.
What patterns of play and combinations he could have worked on in that time is debatable and his predecessor Julen Lopetegui must deserve some credit for delivering Wolves' players through their summer uncertainty to be able to perform as well as they did.
Cunha was outstanding in all aspects but one. His tracking back, runs from deep, and willingness to make space were all top class - but he is a striker and needs to score, and he wasted Wolves' best chance.
After Matheus Nunes' surging run forward, he took up exactly the correct position as Sarabia sent his low cross to the far post.
The angle was not ideal but Cunha opened his body up to give himself the best chance of converting - yet still missed.
Scoring goals has been a problem for Wolves for some time now and amid many issues at Molineux, it is a key one O'Neil needs to solve.
A new season has brought no resolution to two pressing off-field matters at Old Trafford.
The ownership situation, triggered by the launch of a 'strategic review' last November, remains unresolved.
And the future of Mason Greenwood - whose criminal charges were all dropped in the spring but which triggered an internal investigation into his conduct - is yet to be finalised.
Most outsiders expected there would be determination to resolve both matters by now and the absence of clarity brought protests surrounding the issues outside the stadium before the game.
The 'Glazers Out' chants transferred inside the ground and will not go away.
The banners around the Greenwood situation underline the position United find themselves in terms of dealing with someone who legally has done nothing wrong.
-- Courtesy of BBC Sport