United recorded their first away victory under the Dutch boss, winning 2-1 after weathering an early onslaught from the Gunners, when goalkeeper David Da Gea saved one-on-one from Jack Wilshere.
At the start of the second half, a bizarre own goal from defender Kieran Gibbs, who had clattered into goalkeeper Wojciech Szczesny, which forced him off with a hip problem, helped turned the momentum for United, with captain Wayne Rooney clipping home a late second on the break as Arsenal were exposed on the counter.
Although Olivier Giroud, back from three months out with a broken foot, reduced the deficit with a 20-yard drive in stoppage-time, there was to be no grandstand finale to prevent Arsenal slipping to a second straight Premier League defeat.
While the Gunners are down in eighth, United moved up to fourth place.
Chris Smalling helped steer inexperienced defenders Paddy McNair and Tyler Blackett through the match, and van Gaal believes United's tactics were proved to be spot-on.
"That is why I play this formation because now I have to play with two young defenders, yes, it was a risk, but I was sure that Arsenal wants to attack and to press us, then, you know that Arsenal is giving a lot of space away," said Van Gaal.
"And then (Per) Mertesacker and our friend (Nacho) Monreal has to defend
That is why I put (Angel) di Maria against Mertesacker and (Robin) van Persie against Monreal, that is why I changed for (James) Wilson, more pace.
"That is what you are thinking in advance of a match and when it is ending like this, you can be happy."
Arsenal boss Arsene Wenger, though, had complete opposite emotions after watching his side again fail to turn a largely promising performance into an end product.
He said: "Our results are not there at the moment because we lack a bit of maturity defensively and we pay for it.
"Because we were 1-0 down and we wanted to desperately come back, and we forgot our principles a little bit.
"I have to see it (Rooney breakaway goal) again because I was surprised there wasn't anyone there any more.
"We were caught when we had a corner for us because sometimes the players forget the cautiousness because the emotional side of the game takes over."
Wenger added: "I wasn't angry with the players - I have a lot of respect for the energy they put in the game and the spirit they show.
"I am just angry because the players do not get rewarded and our fans do not get rewarded for the result that was just there for the taking."
There where signs of a growing discontent in some sections of the Emirates Stadium crowd.
Manchester United substitute Darren Fletcher was involved in a heated exchange with fans behind the opposition bench following the opening goal, when it is understood a paper cup of coffee was thrown at the visitors as they celebrated the opening goal.
A few Arsenal fans, meanwhile, held up A4-sized placards calling for Wenger's dismissal, which were quickly confiscated by club stewards.
Arsenal captain Mikel Arteta revealed the players were in shock as to just how they did not manage to get something out of the match.
"We played our best game of the season, but it is about being ruthless for sure because when you are inside the box, and you cannot manage to score in that many situations, you cannot expect to win a football game," he said.
Arteta, though, insists Arsenal must not allow any hangovers from such a disappointing result as they prepare for Tuesday night's Champions League tie with Borussia Dortmund.
"When you lose, there is something which is not going well, but we cannot forget (what we have done well) as that creates a lack of belief and confidence if you just take a lot of negatives at the end when you have lost the game.
"We have been too inconsistent at home and dropped too many points already, but we have been saying that for weeks now and we need to turn that around."
Goalkeeper Szczesny was able to walk unaided out of the stadium, while Wilshere had an X-ray on his ankle, which was clear, but will be assessed once the swelling has gone down.
Source : PA
Source: PA