The Danish champions took the lead in the 27th minute at Old Trafford when Pione Sisto confidently slotted home to put the visitors 3-1 up on aggregate.
However, United were soon level on the night when Nikolay Bodurov turned the ball into his own net five minutes later.
Teenager Marcus Rashford then scored twice in 12 minutes on his debut, before Memphis Depay netted and Ander Herrera’s penalty added gloss to the scoreline.
The result will come as a significant boost to Louis van Gaal’s side, who have struggled to find consistent form all season.
And former Red Devils midfielder Scholes was impressed by what he saw from United on Thursday night.
Speaking on BT Sport after the game, Scholes said: “It’s as good as we’ve seen at Old Trafford for some time.
“This club is all about bringing young players through. We’ve seen a special debut from [Rashford] and hopefully he’ll kick on from there.”
He added: “Tonight will mean a lot to [Van Gaal]. He’s not been happy with the performances. It’s a great confidence booster, the young players have been great and Memphis Depay was sensational.
“To score five goals at Old Trafford is entertainment, and that’s what we want.”
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