Rashford scored twice in United's 3-2 win over the Gunners at Old Trafford, his third and fourth senior goals following his UEFA Europa League double on debut against FC Midtjylland on Thursday.
For Van Gaal, the fact the striker followed up his impressive debut with another stellar performance puts him alongside some other greats he has given opportunities to in his storied career, including Muller at Bayern Munich, Barcelona's Xavi and Patrick Kluivert at Ajax, per Jeremy Cross in the Daily Star:
The experience of mine is that youngsters always play well the first match, but the second match is different. But Marcus played well in both matches so he is a special talent.
I can imagine this debut is like a lot of them. Patrick Kluivert makes the winning goal (for Ajax) in the Super Cup in the Netherlands.
Xavi was also fantastic against I think Valladolid (for Barcelona) and also Thomas Muller had a fantastic debut.
It's unbelievable, when you are 18 and come in like that. Four goals in two matches is an average that is unusual.
When you get the chance you have to perform and do the things we are asking. I've always said it's not a matter of age but quality—and he's showed it.
Van Gaal has historically been willing to give chances to youth players in his managerial career, but the introduction of Rashford has been less by design than necessity.
He was initially on the bench for the Midtjylland game, but he was promoted to the starting XI when Anthony Martial got injured in the warm-up.
Rashford seized his opportunity with both hands and proved it was no flash in the pan by putting in an even better performance against much tougher opposition on Sunday.
Per Bleacher Report's Dean Jones, he was the key man for United against the Gunners, not only scoring twice, but setting up Ander Herrera for the third goal:
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Former Red Devil Danny Welbeck—also a graduate of south Manchester's Fletcher Moss Rangers, where Rashford started as a youngster—and Mesut Ozil netted for the Gunners, but they did not have enough to earn a point.
Rashford has shown he has enormous potential and is one of the youngest players to score in the Premier League for United, an impressive feat given the club's history of developing youngsters, per Opta:
18y 120d - Marcus Rashford is the third youngest player to score for @ManUtd in the Premier League (after Macheda & Welbeck). Fresh.2016-2-28 14:36:40
However, it is much too early to assess whether he will become a regular in the first team, as he has to prove he can maintain his impressive form on a consistent basis—as Muller, Xavi and Kluivert all went on to do.
He could not have made a better start to his United career, though, and may have another opportunity to prove himself on Wednesday when the Red Devils host Watford in the Premier League.