The Danish champions led 2-1 from the first leg and Pione Sisto increased their advantage.
Nikolay Bodurov’s own goal reduced the deficit before Rashford, who only started after Anthony Martial was injured in the warm-up, struck twice.
Ander Herrera’s penalty and Memphis Depay’s late goal completed the rout.
Juan Mata missed a penalty at 1-1, while Midtjylland finished with 10 men after Andre Romer was sent off for a second yellow card.
Man of the match – Marcus Rashford (Manchester United)
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