Rashford gave United the win when it seemed the game was heading for a goalless stalemate, with his left-footed shot taking a deflection off Romain Saiss and beating goalkeeper Rui Patricio at the near post.
Rashford acknowledged United ground out the win after a laboured performance although manager Ole Gunnar Solskjaer deployed an adventurous formation with three forwards behind striker Edinson Cavani.
"Today was tough but we expected a tough game and managed to get over the line," Rashford told the BBC. "It's the deciding goal. Probably not the most beautiful but we will take what we can get and move on.
"We can't look too far ahead. We are a team that is still doing a lot of work on ourselves. We have to take it one game at a time but if we can keep finding ways to win like this we will see where we are at the end of the season."
The visitors missed several chances in the first half as they stifled United with crisp one-touch passing but the best opportunity fell to the home side when Patricio kept out a Fernandes sitter in the 34th minute.
Patricio also clawed out a vicious long-range effort by Paul Pogba in the 75th minute and Wolves seemed to have done enough to earn a point after soaking up United pressure in the closing stages.
But they were undone from a seemingly innocuous move as Rashford picked up a long Fernandes pass on the right, cut inside and with little support in the penalty area, he hit a hopeful shot which wrong-footed Patricio.
Wolves manager Nuno Espirito Santo rued his team's lapse of concentration in the dying minutes but added they needed to put the disappointment behind them quickly amid a busy festive schedule.
"This is football and a learning process," the Portuguese told Amazon Prime. "It's cruel in the moment but you can't stay feeling sorry. You have to move forward. We created chances. Sometimes we should finish more."