Hitzfeld said before the Spanish match that Switzerland's striker and record goalscorer Frei would resume training on Thursday after an ankle injury ruled him out of their first Group H game in Durban on Wednesday.
Sticking with two up front, Hitzfeld drafted in Eren Derdiyok to play alongside Blaise Nkufo. Derdiyok is a tall, powerful striker who was instrumental in creating the winner against Spain by Gelson Fernandes in the 52nd minute.
"When we lost Alex Frei to the injury, I decided quite spontaneously to put my money on Eren Derdiyok," said Hitzfeld.
"We knew we had to have a very strong forward there, a very strong striker, someone who can create confusion in the opponents defence," the German coach said after the match.
Stand-in captain Gokhan Inler marshalled the Swiss midfield well, carrying out Hitzfeld's plan expertly to shut Spain out of the "red zone" between defence and the middle of the park.
Inler has been the mainstay of Switzerland's midfield since Hitzfeld took the job and the German coach praised his performance, saying he was "extremely important".
"I'm very happy, I'm very satisfied about this excellent start. That is precisely what we need to go into the match again Chile with resolve," said Hitzfeld, who has won the Bundesliga seven times as well as two Champions League titles.
"Chile will be just as difficult to play as Spain. And I'm sure my team will now go into the match with a great deal of self-confidence, which we need to tackle the more difficult issues that lie ahead," he said.
"To overcome Chile we've got to go beyond what we've shown today," Hitzfeld added after the game.
