United got the better of Premier League rivals Wolves 1-0 at home in the FA Cup third-round replay.
Juan Mata scored the only goal of the match midway through the second half at Old Trafford when he chipped the ball over Wanderers goalkeeper John Ruddy after Anthony Martial put him through on goal.
Rashford did not start the match, but the England international forward came on as substitute in the 64th minute.
However, the 22-year-old suffered a back injury and was substituted 10 minutes from the full-time whistle.
The youngster is delighted with the win for United, and he has stated on Twitter that he tried his best to carry on playing despite his injury.
Never want to feel like Ive let my teammates, the club and most importantly the fans down so did my very best to carry on tonight and was gutted to come off.
— Marcus Rashford (@MarcusRashford) January 15, 2020
Top work from the lads to get into the next round pic.twitter.com/ZLpxiqhtq3
Stats
Over the course of the 90 minutes at Old Trafford on Wednesday evening, hosts United had 57% of the possession, took 11 shots of which six were on target, and earned six corners.
Visitors Wolves had 43% of the possession, took seven shots of which two were on target, and earned five corners.
United will return to action on Sunday when they take on Liverpool away from home at Anfield in the Premier League.
The Red Devils will face either Watford or Tranmere Rovers away from home in the fourth round of the FA Cup on January 26.