Stephan Lichtsteiner and Xherdan Shaqiri both scored in the final 12 minutes as Switzerland accounted for Peru in an international friendly at the Swissporarena in Luzern.
It was Switzerland's second win in less than a week after Friday's narrow 1-0 victory against Jamaica.
"I am pleased that we have won," the 65-year-old said.
"At the beginning of the game was felt among the players the fatigue of the nine-day training camp. Finally, we have but the game deserved to win.
"We have trained hard and set a good base. The fact that we have won twice is good for morale. We are on the right track."
"It's fantastic to see that (such a) defender as Lichtsteiner score a goal. He not only has erased many fires back, but made a wonderful goal," said Hitzfeld.
"If the enemy is tired, he is fantastic," he added. "I assume that Shaqiri can be fully fit in Brazil."
