Rashford's shot deflected into Rui Patricio's goal with less than two minutes remaining.
The away side can feel hard done by, as they severely tested United stopper David De Gea, especially in the first half.
United are now cemented firmly in second place in the table going into the new year.
So who were the standout performers?
✔️ GOOD PERFORMANCE
Ruben Neves: 7.0
The Portuguese midfielder was in splendid form at Old Trafford, and forced United stopper David De Gea into a fine save in the first half with a rasping shot from distance.
Neves recovered the most balls throughout the game, and kept Wolves ticking with his passing. Neves completed 84% of his 56 passes during the game, and was threatening numerous time throughout the game.
❌ BAD PERFORMANCE
Adama Traore: 6.1
Traore was handed a rare start this season by boss Nuno Espirito Santos, but he didn't repay his manager with a stellar performance.
Traore produced the performance of a player short on confidence. The Spaniard got himself into some promising positions, but his end product was disappointing.
He somehow lasted on the pitch throughout the entire game, but it wasn't a performance that will convince Espirito Santos to give him more first team opportunities.
Perhaps his time at Molineux is over?
⭐ STAR MAN
David De Gea: 8.0
It's a return to form for the Spanish goalkeeper, who made several vital saves to keep United in the game.
Despite Rashford's late winner in the dying minutes of the game, it's due to De Gea that Solskjaer's side picked up the three points, and kept themselves within two points of Premier League leaders Liverpool.