The Netherlands appeared to be heading for the FIFA World Cup exit door after Giovani dos Santos had given Mexico the lead in Sunday's last 16 clash in Fortaleza.
However, midfielder Wesley Sneijder equalised two minutes from the end of normal time and substitute Klaas-Jan Huntelaar netted the winner from the spot in injury time after Arjen Robben won a controversial penalty.
Kuyt started the game at right-back before making the move up front as Van Gaal changed his system in search of a way back into the contest.
However, Van Gaal's key decision came in the 76th minute, withdrawing star striker Van Persie in favour of Huntelaar; a move that paid dividends as the latter kept his composure to slot into the bottom corner from 12 yards.
And Fenerbahce man Kuyt feels that the 62-year-old - who will take over at Manchester United after the World Cup - is the most tactically astute coach in the game.
"He's maybe the best tactically there is in the world," Kuyt said.
"It doesn't matter what system we are playing the players know exactly what to do.
"He told us before the game already that we could switch system if we were 1-0 down.
"We switched to 4-3-3 then 15 minutes before the end of the game he decided to put an extra striker to play longer balls and look for second balls and we managed to score a goal so his tactics were once again spot on."
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