A superb goal from Juan Mata after half-time saw United finally get the better of Wolves and seal our place in the FA Cup fourth round.
The diminutive Special Juan clipped over John Ruddy to settle this third round replay, having been put through by Anthony Martial.
In a tight game at Old Trafford, with little between the two sides as usual, United deserved their win and will now face either Watford or Tranmere away next.
The result was overshadowed by a worrying injury to Marcus Rashford who limped down the tunnel clutching his side only 14 minutes after coming on. The concern over the Reds main man is only heightened by the prospect of him being ruled out for Sunday's daunting trip to Liverpool.
Wolves had an early Pedro Neto strike ruled out by VAR after a handball in the build up. Raul Jimenez had jostled with Harry Maguire, his outstretched hand had changed the direction of the ball and teed up Neto to run through and score.
Ole Gunnar Solskjaer's side had failed to muster a shot on target in the goalless first game between the two sides, but were much more threatening this time around.
Ruddy saved well from Mata early on, with Dan James also denied smartly by the impressive Wolves keeper.
After a frenetic start, the game lapsed into a familiar pattern but ageing Mata, 31, rolled back the years with one moment of quality in a clever finish.
Solskjaer named a stronger than expected side - as, to be fair, did our opponents - with the games coming thick and fast and that trip to unbeaten league leaders Liverpool only three days away.
But the United manager will know that this cup probably represents our best chance of silverware with the Carabao Cup out of reach and the Europa League a long shot.
Eager to get the job done and finish the tie inside the 90, Solskjaer sent on talismanic figurehead Rashford to add bite to the attack and the Reds were ahead within three minutes of his arrival.
But the gamble to involve Rashford might prove costly as our top scorer pulled up injured and had to be replaced by Jesse Lingard. Solskjaer admitted it had backfired after the game as United are now left sweating on the fitness of the forward.
Martial flashed a shot wide and Raul Jimenez was off target before VAR intervened again. Fred's wild mishit pass struck Nemanja Matic and fell to Jimenez, only for the ball to brush his hand and rule out Neto's subsequent finish. It seemed harsh as the Mexican knew little about it, but the new rules stipulated that the goal had to be disallowed.
Martial put an effort wide and Fred tried his luck from distance whilst Wolves posed an intermittent threat at the other end.
Ruben Neves had a trademark effort from distance well saved by Sergio Romero and Conor Coady should have done better with a header. The centre back nodded wide from ten yards when well placed after Jonny Castro Otto had picked him out.
Neves smashed an effort wide and Matt Doherty headed a pass from the same player off a post, with Jimenez flagged for offside on the rebound.
Mata went close again and Neves smashed one over the top over in an increasingly end-to-end contest.
Substitute Andreas Pereira forced a save out of Ruddy on the counter-attack, with Maguire solid at the back and the Argentina stopper keeping yet another clean sheet.
Overall team performance: 7/10
United Faithful Man of the Match: Brandon Williams