The result left United on 30 points from 15 games, two behind champions and leaders Liverpool who visit Newcastle United on Wednesday, while Wolves stayed 12th on 21 points.
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".