A lovely goal from Juan Mata enlivened another dull game and was enough to take Manchester United into the fourth round, in which they will travel to Watford or Tranmere.
Wolves, on the other hand - who were disappointing in both legs - must now focus on the Europa League, in which they meet Espanyol next month.
The game actually started surprisingly well, with both sides looking lively in the opening half-hour; United had more of the ball and created two decent chances, but fine saves from John Ruddy and poor finishing from Daniel James ensured their score stayed at nil.
Wolves, meanwhile, ought to have gone ahead on nine minutes when Raul Jimenez skinned Brandon Williams inside the box, only to dribble a weak shot too close to Sergio Romero. Then, just a minute later, Pedro Neto had the ball in the net after Jimenez capitalised on a signature careless pass from Fred, but the goal was ruled out when VAR showed that it had struck the Mexican's hand on its way across the box.
United were by far the better side after the break, without threatening or creating much until, on 67 minutes, Harry Maguire robbed Matt Doherty and fed Anthony Martial, who times his ball perfectly, meeting Juan Mata's run; somehow, Mata stayed ahead of the chasing defenders, sat Ruddy down, and lifted a fine finish over him and into the net.
Juan Mata (Getty)
Image credit: Getty Images
Wolves created little in the remaining time, during which Marcus Rashford, on as sub, went off with a bang to the back - though he should be fine for the weekend - and then, in the final seconds, Ruben Vinagre seemed to twang his hamstring, capping a miserable night for the old gold.
Midfield? Pah! Manchester United have a serviceable defence and an exciting forward line, but the state of their midfield is a humiliation. They cannot adequately protect their back four, nor can they adequately service their strikers.
MAN OF THE MATCH
Brandon Williams (Manchester United) Another energetic and aggressive performance. He still has plenty to learn, but United are so much better with him than with Luke Shaw or Ashley Young.
Manchester United: Romero 6, Wan-Bissaka 7, Lindelof 6, Maguire 7, Williams 7, Matic 5, Fred 5, Mata 7, Greenwood 5, Martial 6, James 6. Subs: Pereira 6, Rashford 6.
Wolverhampton Wanderers: Ruddy 7, Dendoncker 6, Coady 6, Saiss 6, Doherty 6, Moutinho 5, Neves 5, Jonny 5, Traore 5, Jimenez 5, Neto 5. Subs: Gibbs-White 6, Vinagre 6, Buur 6.
Mason Greenwood of Manchester United in action with Conor Coady and Leander Dendoncker of Wolverhampton Wanderers during the FA Cup Third Round Replay match between Manchester United and Wolverhampton Wanderers at Old Trafford on January 15, 2020 in Manch
Image credit: Getty Images
9’ CHANCE! Great chance for Wolves! Traore gets himself one on one v Mata, who bulldozes through him ... not really. A stepover and he's gone clipping back a cross that Jimenez takes beautifully before Cruyff-turning away form Williams only to dribble a shot straight at Romero from bang in front of the posts.
10’ GOAL! Manchester United 0-1 Wolverhampton Wanderers (Neto) Awful from Fred, the most careless player in the world. He whumps a pass into Matic, the ball falls to Jimenez, and as Maguire ploughs in he squirts through to Neto, who sits Romero down and passes home the opener.
11’ GOAL DISALLOWED! When Maguire challenged, the ball bounced off Jimenez's arm. The law is a nonsense - if it's accidental and that was, let the game go - but has been correctly applied.
42’ CHANCE! United's best chance of the game! Another ball clipped over the top, this time by Fred - with his right foot! - puts James in on goal! He takes it down nicely too, but without a goal since September, he just drives it into the keeper's body - though Ruddy did well to stand up for as long as he did.
52’ CLOSE! Excellent from United, Martial wandering wide and feeding Williams, who plays a lush, disguised ball into the box that James allows to run past him ... he's in, wide of goal, but in space, and he cracks a low shot this much wide.
67’ GOAL! Manchester United 1-0 Wolverhampton Wanderers (Mata) That Wolves attack breaks down and Maguire is allowed time to pick and sling a long ball down the left channel for Martial, who ducks inside, ahead of Coady, waits ... and waits ... before slipping Mata in! Like a geriatric spaniel, he drives for the box, feints to shoot and sits Ruddy down, then sinks a lovely finish into the net. Very well taken indeed.
In Brandon Williams' last seven appearances, United have kept six clean sheets.
Juan Mata has been involved in three goals in his last two appearances, as many as in his 20 previous appearances this season.