Oranje were 1-0 down with just two minutes of time remaining, before Wesley Sneijder's strike and a Klaas-Jan Huntelaar penalty turned the game on its head to send the Dutch into the quarter-finals.
The game in Fortaleza saw FIFA's pre-arranged three-minute breaks midway through each half used for the first time.
"Yes, I used the breaks," Van Gaal is quoted as BBC Sport. "First I had changed from 4-3-3 and then we created a lot of opportunities, the shot on the goalpost and a fantastic save by Ochoa. Then I moved to plan B and yes, I did that in the cooling break that is a clever way of benefiting from these breaks."
The Netherlands will now face the winner of tonight's meeting between Costa Rica and Greece.