United rode their luck in the first half as Brentford dominated, forcing a number of important saves from goalkeeper David De Gea. But Ralf Rangnick’s side were clinical after the break, with goals by Anthony Elanga, Mason Greenwood and Rashford securing a flattering victory.
Brentford should have been comfortably ahead by halftime but spurned numerous chances and were made to pay for their wastefulness when Elanga nodded United in front on 55 minutes.
Greenwood tapped in from a counter-attack shortly after, and substitute Rashford rifled in his side’s third in the 77th minute to leave Brentford stunned.
Ivan Toney pulled a goal back from close range with five minutes remaining but it was scant consolation for the hosts who slumped to a third successive defeat.
Brentford remain in 14th place, 10 points above the relegation places.