Rashford’s name was not listed in the United squad in the programme, he was called into the starting XI at the last minute before the game to replace Anthony Martial, who suffered a hamstring injury in the warm-up to the game.
The youngster, however, scored twice before an Ander Herrera penalty and a Memphis Depay strike moved United into Friday’s last-16 draw.
“I wasn’t worried about him. I’m always confident for that,” said Dutchman Van Gaal. “He was the best option.”
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Rashford had not started a game above under-19 level for United and his most recent goal was for the club’s Under-18s in mid-February.
Louis Van Gaal’s side, who suffered a humiliating 2-1 win at Denmark, did not get off to an ideal start as the visitors opened the scoring in the 27th minute through Pione Sisto to further stretch the tie.
The home side however, responded swiftly with as Memphis Depay’s cross was deflected into the net by Nikolay Bodurov, and they were close to level the tie when Juna Mata missed a penalty just before the break.
The Red Devils started the seconf half on a stronger note, as Rashford scored his first in the 63rd minute following a pass from Mata, to level the tie, and the teenager was slotted home in similar style to put Louis Van Gaal’s side in front for the first time in the game.
Midfielder, Ander Herrera and Depay decided the tie in the closing stages, with Midtjylland reduced to 10 men in the 89th minute following Andre Romer’s dismissal.
The result means United are now through to the last 16 of the Europa League, to ease some of the pressure on Van Gaal.
Both Liverpool and Tottenham also came out victors on the night, to advance to the last 16.