An Ashley Young brace and a late Javier Hernandez header sealed the 3-1 win in the International Champions Cup in front of nearly 110,000 fans at the Michigan Stadium, setting up a final against traditional rivals Liverpool in Miami on Monday.
The win was United's fourth on the pre-season trip to the USA, but it was the quality of the performance which gave van Gaal the most satisfaction as his side continue to make the new 3-4-1-2 formation work.
Van Gaal had particular praise for his defenders, who the Dutchman says have had to make the biggest adjustment.
"It's amazing that you can pick up a new system like that," said van Gaal, who used the formation in the knockout stages of the World Cup with the Netherlands.
"It's not a new system for Juan Mata, Wayne Rooney or Danny Welbeck, who play in their position, neither is it a new system for the two midfielders.
"The greatest impact with this new system is on the back line. It's amazing we had one chance against us in the first half, and two in the second."
Van Gaal said his side's victory over the Champions League winners was much more significant than just a pre-season friendly.
"It's a very good result for us and it gives confidence to all the players," said van Gaal.
"The game was not a friendly; I had the feeling that Real didn't want to lose, which is why they started with Ronaldo a little bit earlier than we expected.
"We deserved to win. We are in the right way and we're missing players like Marouane Fellaini, Adnan Januzaj and Robin van Persie."