Manchester United moved into the top four of the Premier League table, after a 0-1 win in the New Year's Eve early kick-off.
After a fairly even first half, with the visitors having the slightly better of the chances, the game was well-poised for the second half.
Towards the end of the 90 minutes, Wolves began to slightly drift out of the contest, as Man United began to look like the team likely to break the deadlock.
The man to score the winning goal was Marcus Rashford - the in-form forward was dropped from the starting 11, due to disciplinary reasons, as briefly mentioned by Erik ten Hag.
Rashford was brought on during the half-time break.
The super-sub's powerful run and neat one-two with Bruno Fernandes led to him firing the ball into the back of Wolves' net from close range. Rashford also had a second goal disallowed for handball late on.
The win puts Man United up into fourth place - two points ahead of Tottenham - with both teams having played 16 games each.
Wolves, unable to kick on from the dramatic away win at Everton, remain in the relegation zone, in 18th place.
Story of the match
There was a single change in the Wolves team, from the aforementioned 1-2 win at Everton.
Matheus Nunes came in to make up an all-Portuguese midfield alongside Ruben Neves and Joao Moutinho, taking the place of Joseph Hodge.
An unchanged Man United team was expected from ten Hag. However, that disciplinary issue meant that Rashford dropped to the bench for the fixture. He was replaced in the 11 by Alejandro Garnacho.
The first action of the game came following a Man United corner.
Casemiro's glanced header was heading on target, but a touch off of a Wolves player redirected the ball just over the bar, preventing Jose Sa from being called into action.
The first quarter-of-an-hour passed without a great deal of drama in front of either goal.
It was not until just after that point, when an under-hit back-pass from Nelson Semedo to Jose Sa provided Garnacho with a clear-cut chance to open the scoring.
The winger's low, first-time effort was very well kept out by the keeper.
A crucial block from Aaron Wan-Bissaka prevented Moutinho from getting through an effort on goal, from inside of the Man United box.
Less than a minute later, the Portuguese midfielder played in Diego Costa and after taking the ball past Raphael Varane, the forward would have been disappointed to only be able to get off a tame effort on goal.
Just as it seemed that Wolves would begin to gather some momentum in the contest, the visitors provided some more evidence of their attacking threat.
On the right wing, a precise through ball from Antony down the line picked out the run of Bruno Fernandes.
The midfielder played a smart, low cross into the path of the oncoming Anthony Martial, who was excellently challenged by Nathan Collins.
The centre-back ensured the forward did not get an effort on goal away.
Raphael Varane added to the list of important blocks being made.
He prevented Daniel Podence's left-footed volley from reaching David de Gea.
Shortly after, a header from Antony only managed to pick out Sa.
The Brazilian had a huge chance to break the deadlock, right before half-time - his header from close range was excellently kept out by the keeper.
However, as Antony was offside, the score would have remained level at the break, even if the ball had found the back of the net.
There was a change each during the half-time break for both teams.
The now-disciplined Rashford came on in place of Garnacho. Adama Traore replaced Costa.
A couple of threatening runs down the right wing within the first few minutes of the restart reflected an instant impact from the powerful Wolves winger.
However, the first threatening moment of the second half fell to the visitors.
Sa came off his line very well to smother a potential attempt at goal from Antony, as the ball deflected to him from a blocked Fernandes attempt.
De Gea's first bit of work in the second period came, when he was tested by a long-range free-kick from Neves. From around 35 yards from goal, a powerful, whipped effort from the midfielder forced the keeper to make an impressive, diving stop to redirect the fantastic strike for a corner.
Just after the hour mark, with his last action of the match, Semedo ensured that his team stayed level. A crucial, glancing header meant that Antony's threatening cross could not be tapped in at the back post, by an oncoming Luke Shaw.
From that point, it was the visitors who had began to control much of the possession and looked like the team more likely to get the crucial first and, likely, winning goal. They did just that, in the 76th minute.
Rashford picked up the ball on the left side. While on his way inside, he played a neat one-two with Fernandes, evaded the challenge of Collins and outmuscled Jonny Otto.
Once in the box and in a dangerous position, he unleashed a powerful strike from close range, which left Sa with little chance of saving his team.
It seemed as if Rashford doubled his own and his team's tally in the 84th minute to kill the game off.
However, as his own shot rebounded back to him, a touch off of Rashford's arm meant that the goal was correctly ruled out and Wolves remained in the game.
Just before the clock ticked over into five minutes of added time, a Man United counter-attack resulted in an effort on goal from outside of the box for Fernandes - a slightly disappointing outcome, given the initial danger of the breakaway.
Three corners built up the late pressure on Man United's goal.
The second of those resulted in a free header for Raul Jimenez, which, unfortunately for the hosts, was directed straight at de Gea.
Barring that troublesome moment, the visitors saw out the final moments of the match with relative comfort and moved back into the top four.
Player of the match - Marcus Rashford
Whatever the detailed reason is for Rashford's exclusion from the starting 11, the in-form winger ensured that did not disrupt his impressive on-pitch performances.
All of the visitors' backline, as well as the two goalkeepers, put in solid showings in this fixture. However, with Rashford's brilliant goal being the difference between the two teams, it is the match-winner who warrants this title.
