Andreas Pereira put Man Utd ahead on 17 minutes, with his low shot taking a deflection off Dale Stephens to wrong-foot Mat Ryan.
The lead was doubled two minutes later, Harry Maguire heading Fred's free-kick towards Scott McTominay, whose bundled effort was deflected in by Davy Propper.
Lewis Dunk pulled a goal back in the 64th minute, powerfully heading in from substitute Pascal Gross's corner.
But Rashford restored Man Utd's two-goal lead two minutes later, smashing the ball in off the crossbar.
United move up to seventh with 16 points, one ahead of Brighton, who drop to 11th.
Man Utd: 24 Nov v Sheff Utd (A)
Brighton: 23 Nov v Leicester (H)