The Real Madrid striker scored his third goal of the tournament in the tie, with Olivier Giroud, Blaise Matuidi, Mathieu Valbuena and Moussa Sissoko also finding the net, as the Swiss only managed two late goals from Blerim Dzemaili and Granit Xhaka in response.PHOTOS: Beautiful people in Brazil | Brazil protests | Soccer fanatics | Fan tattoos
Benzema has recently endured some barren spells for France, once going 15 matches and 1,222 minutes without scoring for les Bleus from June 2012 to October 2013, but is now delighting in his form, though claiming he can still give more.
"I am in my head 100 percent, but I can do better," the 26-year-old was quoted as saying by France Football. "I also [reap the benefits of] the work of my teammates. It's not [just] me, it's everyone. Even those who did not start the first game and who returned to this one.
"Oliver [Giroud] and I have confidence that whenever we play together, we will have an understanding. After that, it's not Karim or Olivier, it's everyone who pulls the team up.
Benzema, who has now struck eight times in his last nine games for Didier Deschamps' side, was named man of the match for a second game in succession and insists he is brimming with confidence for what les Bleus can achieve.
"Since the beginning, I have had dreams," he said. "I have goals in mind. Gradually, you get there. I've been convinced that we will get better for a while.
"I am happy and proud. It was a big game, we scored goals, we played as a team. We gave our answers on the pitch. We had heart to win that game. We're very pleased with the performance and we'll try to repeat it against Ecuador."
France now faces Ecuador on June 25 in its final Group E game.