Match ends, Manchester United 1, Wolverhampton Wanderers 0.
Juan Mata's superb second-half goal sent Manchester United into the FA Cup fourth round as they beat Wolves.
The Spanish midfielder chipped over keeper John Ruddy to settle the third-round replay after being put through on goal by Anthony Martial.
Wolves had an early Pedro Neto strike ruled out by the video assistant referee for a handball in the build-up.
But it was a deserved win for the hosts, who had the better chances in a tight game at Old Trafford.
Manchester United will next travel to either Watford or Tranmere - whose third-round replay at Prenton Park on Tuesday was postponed because of heavy rain.
Ole Gunnar Solskjaer's side did not manage a shot on target in the goalless first game between the two sides at Molineux on 4 January but were much more threatening in this match.
An excellent save by Ruddy prevented Mata from opening the scoring in the first half, while Daniel James was also denied by the Wolves keeper.
After a high-tempo start, the game settled down - but Mata, 31, produced the one moment of quality to seal victory, rolling back the years with a clever finish.
Man Utd get job done but at a potential cost
It is a tough period for many clubs in the Premier League with games in multiple competitions coming thick and fast. With his side facing a tough trip to league leaders Liverpool on Sunday, Solskjaer may have been forgiven for making numerous changes for this tie.
But the FA Cup and Europa League arguably represent Manchester United's most realistic routes to trophies this season and Solskjaer underlined how seriously he is taking this competition by naming a strong line-up on Wednesday.
There were just three changes from the side that beat Norwich 4-0 in the Premier League last Saturday, as Sergio Romero was named in goal, while James and Mason Greenwood also started.
Wolves, too, went strong with their line-up, with Ruddy their only change and the two sides, cancelled each other for large periods.
Eager to get the job done and wrap up the game inside 90 minutes, Solskjaer sent on top scorer Marcus Rashford in the 64th minute to add bite to his attack and, three minutes later, United were ahead.
But the gamble to involve Rashford may prove costly; the striker pulled up with an injury and had to be replaced by Jesse Lingard just 16 minutes after coming on.
After the game, Solskjaer admitted the decision to play Rashford was one that backfired.
'You can't celebrate' - Coady furious with disallowed goal
VAR has certainly had its critics this season - but for the second time in five days, it was new regulations relating to handball that caused controversy as the video official stepped in to rule out a goal.
The law regarding handball, updated before the start of this season, states any goal scored or created with the use of the hand or arm will be disallowed "even if it is accidental".
West Ham and Declan Rice fell victim to it last Friday when the midfielder's injury-time equaliser against Sheffield United was ruled out because the ball had touched his arm in the build-up.
This time, the handball rule was applied early on at Old Trafford when VAR spotted that the ball had brushed Raul Jimenez's hand just before Neto fired home early on.
It was a let-off for Manchester United and spared Fred's blushes with the strike having come as a result of a wild pass by the midfielder that deflected off a team-mate and into Jimenez's path.
It also seemed to set the tone for the rest of the game as Manchester United grew in confidence after a strong start by Wolves, who struggled to get Adama Traore involved as much as they would have hoped.
After the game, Wolves captain Conor Coady said: "It's constant, all we are talking about is VAR. It's ridiculous, it's stupid.
"You can't celebrate. Raul Jimenez didn't even know he had handballed it. We have to get used to it.
"All of it is terrible for me. It's not for me, it's not for a lot of players. But people higher up in the game are happy with it."
Man of the match - Brandon Williams (Manchester United)
Manchester United boss Ole Gunnar Solskjaer: "I think you can see it was two teams towards the end that were tired. It was end to end and an open game - sometimes that doesn't suit us.
"We're delighted to beat Wolves finally. Juan Mata is different class. He's got the skill, composure and even pace."
Wolves boss Nuno Espirito Santo: "It was a good game of football, an even game. Both teams had chances.
"We didn't defend the goal well but we reacted well and were in the game. A proper game, I am disappointed to go out because it is frustrating when you perform well and go out."
On the disallowed goal: "That's VAR, you cannot do anything about it. We are celebrating non-goals - it doesn't make sense."
Another early exit for Wolves - the stats
- Manchester United have won each of their past six home matches in the FA Cup without conceding a single goal in this run.
- Wolves have been eliminated at the third-round stage or earlier in seven of their past nine FA Cup campaigns, this after having made it to at least the fourth round in each of their nine seasons in a row before this.
- Manchester United have won nine of their past 10 home matches against Wolves in all competitions, keeping six clean sheets in those games.
- Juan Mata has been directly involved in three goals in his past two games for Manchester United (one goal, two assists), as many as he was in his first 20 appearances of the 2019-20 season in all competitions before this.
- Since his FA Cup debut in January 2016, Manchester United forward Anthony Martial has eight assists in the competition. Only Peterborough's Marcus Maddison (11) has more in this time.
- Marcus Rashford was the first Manchester United player to both come on as a substitute before then being substituted himself in the same FA Cup match since Alan Smith against Liverpool in February 2006
Manchester United travel to Premier League leaders Liverpool on Sunday, 19 January (16:30 GMT) while Wolves are at Southampton the day before (15:00).
- 5MaguireBooked at 74mins
- 17FredBooked at 37mins
- 26GreenwoodSubstituted forPereiraat 64'minutes
- 21JamesSubstituted forRashfordat 64'minutesSubstituted forLingardat 80'minutes
- 32DendonckerBooked at 84mins
- 28João Moutinho
- 19Castro OttoSubstituted forVinagreat 75'minutes
- 7NetoBooked at 59minsSubstituted forGibbs-Whiteat 71'minutes
- 37TraoréSubstituted forBuurat 88'minutes
- 11Rui Patrício
- Kevin Friend
- Shots on Target
Second Half ends, Manchester United 1, Wolverhampton Wanderers 0.
Attempt saved. Andreas Pereira (Manchester United) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Anthony Martial.
Offside, Manchester United. Jesse Lingard tries a through ball, but Anthony Martial is caught offside.
Harry Maguire (Manchester United) wins a free kick in the defensive half.
Foul by Raúl Jiménez (Wolverhampton Wanderers).
Offside, Wolverhampton Wanderers. João Moutinho tries a through ball, but Oskar Buur is caught offside.
Attempt missed. Romain Saïss (Wolverhampton Wanderers) header from the centre of the box misses to the left. Assisted by João Moutinho with a cross following a corner.
Corner, Wolverhampton Wanderers. Conceded by Victor Lindelöf.
Offside, Wolverhampton Wanderers. Raúl Jiménez tries a through ball, but Morgan Gibbs-White is caught offside.
Substitution, Wolverhampton Wanderers. Oskar Buur replaces Adama Traoré because of an injury.
Corner, Manchester United. Conceded by Rúben Neves.
Leander Dendoncker (Wolverhampton Wanderers) is shown the yellow card for a bad foul.
Aaron Wan-Bissaka (Manchester United) wins a free kick in the defensive half.
Foul by Leander Dendoncker (Wolverhampton Wanderers).
Attempt missed. Rúben Neves (Wolverhampton Wanderers) right footed shot from outside the box is too high. Assisted by João Moutinho following a corner.
Corner, Wolverhampton Wanderers. Conceded by Victor Lindelöf.
Anthony Martial (Manchester United) wins a free kick on the right wing.
Foul by Romain Saïss (Wolverhampton Wanderers).
Substitution, Manchester United. Jesse Lingard replaces Marcus Rashford because of an injury.