Marcus Rashford stepped off the bench to earn United a hard-fought fifth successive win and lift Erik ten Hag's side into the top four.
Rashford; dropped for disciplinary reasons; came on at the interval and struck his eleventh of the season - and third goal in as many games - in new Wolves manager Julen Lopetegui's first home game at the helm.
Molineux has traditionally been an unhappy hunting ground for United and despite the old Gold's current struggles at the wrong end of the Premier League table, this would prove no different.
After Newcastle's goalless stalemate with Leeds and City's 1-1 draw with Everton, the Reds sit a place and two points behind Eddie Howe's high flyers with a game in hand. Guardiola's slickers are currently in second place, but only four points ahead of us.
There was one charge to ten Hag's side from the XI which beat Wanderers relegation rivals Nottingham Forest on Tuesday as Alejandro Garnacho came in for Rashford.
In United's final fixture of a largely forgettable 2022, our red hot no.10 showed great strength to hold off a posse of players and drill home an excellent finish 14 minutes from the end.
United will go into the New Year in fourth place; two points behind Newcastle with a game in hand and only four off Pep Guardiola's faltering City.
The influential Casemiro had a header deflected over in the sixth minute before an excellent piece of last-ditch defending saw Nelson Semedo snuff out the danger from a lurking Garnacho.
The Wolves right-back then underhit his backpass to the feet of the forward, but the teenager was thwarted by the smart reactions of keeper Jose Sa.
The home keeper was soon called into action again to keep out Antony's deflected effort, before both sides were indebted to brilliant pieces of defensive play. First, the much-maligned Aaron Wan - Bissaka came to the Reds rescue when his lunging block prevented a certain goal from Joao Moutinho. Minutes later, James Collins was on hand to deny Anthony Martial a clear opening after his excellent challenge meant the Frenchman couldn't turn home a Bruno Fernandes cross.
Sa saved well from Antony on the stroke of half-time when the Brazilian winger perhaps should have done better.
Rashford was summoned off the naughty step whilst Wolves also upped the ante with speedster Adama Traore on in place of the Reds old nemesis Diego Costa. With Luke Shaw at the heart of a makeshift back four, Traore was tasked with unsettling the Reds' defence and pinning us back.
Clear cut chances were few and between as the Reds' annual visit to Molineux lapsed into a familiar, jarring pattern. Fernandes fired over from a free-kick before compatriot Ruben Neves almost showed his Portugal team-mate how it's done, only for David de Gea to produce an excellent full-length save.
Struggling Wolves face a battle for survival and Lopetegui must find the answer to his new team's problems in front of goal. United also have well-documented issues in that department but came up with the solution here in the shape of the red-hot Rashford.
A give-and-go between Rashford and Fernandes saw the latter release the former to show great strength and perseverance as he cut inside to hold off three players and fire in under the stranded Sa.
Our super sub thought he had put the result beyond doubt minutes later when Wan - Bissaka picked him out. Rashford's shot was saved by Sa only for the ball to rebound in off the onrushing Rashford only for VAR to chalk the goal off for handball.
That set up a frantic finale in which de Gea saved superbly from substitute Raul Jimenez, and Ruben Neves had a drive deflected narrowly wide in the final moments.
United survived through five harum scarum minutes to hold out for victory and ensure a perfect ending to 2022. A third straight win (and clean sheet) for United since the restart and a clear upward trajectory. Roll on 2023.
Overall team performance: 6/10. Job done
United Faithful Man of the Match: Marcus Rashford MBE.