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.
Hitzfeld said he was pleased with the performance as the Swiss prepare to face France, Ecuador and Honduras in Group E at the World Cup.
"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."
Hitzfeld also reserved special mention for goalscorers Lichtsteiner and Shaqiri.
With the game seemingly petering out to a draw, Juventus defender Lichtsteiner rose highest to head home the 78th-minute opener - his fifth goal for the national team.
"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.
Bayern Munich midfielder Shaqiri came off the bench on the hour mark and put the result beyond doubt six minutes from time.
It was a welcome boost for Shaqiri, who has been hampered by injuries for most of the season, though Hitzfeld is confident the 22-year-old will be fit for the showpiece event.
"If the enemy is tired, he is fantastic," he added. "I assume that Shaqiri can be fully fit in Brazil."
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