Federer showed no signs of fatigue despite playing just two days after retaining his Wimbledon crown with victory over American Andy Roddick.
After arriving in the Alpine resort late on Monday, the Swiss world number one comfortably moved into the second round of the tournament, where he finished runner-up last year.
Federer, who has won six titles this season, outclassed the Brazilian-born German Behrend, who won just two games and was broken four times against the tournament's top seed.
Federer had earlier received a standing ovation and was presented with a traditional, three-metre-long, Swiss alphorn as reward for his Wimbledon victory.
In the Roy Emerson Arena, Federer was prompted to play the trumpet-like instrument traditionally used to herd livestock.
"Somehow I did the right thing at the right moment," Federer said of his immediate mastery of the technique. "But then I had to pose again for photos and I tried to do it again and then it didn't work.
"I knew before that I wouldn't be getting a cow. I've got two already, I don't need a third. They knew that and I was relieved."
In other matches on Tuesday, second seed Juan Carlos Ferrero was upset by Austria's Stefan Koubek 7-6, 6-4, while fifth seed Andrei Pavel of Romania was beaten by Switzerland's Davis Cup captain Marc Rosset 7-6, 6-4.
Ferrero, the 2003 French Open champion and a claycourt specialist, struggled on the clay at Gstaad and lost the first set tiebreak 7-4 before he was broken in the second set.
"I'm not playing my best tennis," said Ferrero, who holds a 4-3 record on his favourite surface this year. "I cannot find my game, I'm sadly lacking confidence."
Rosset, the 1992 Olympic champion who is contemplating retirement, said the match had taken a toll on his 33-year-old body.
"I played a two-set match like it was a 400-metre race. I can't keep going like this," he said.
Ferrero's compatriot David Ferrer progressed into the second round with a 2-6, 6-3, 6-4 victory over Tomas Berdych.
Third-seed Rainer Schuettler also progressed with a 6-4, 1-6, 6-3 victory over Michel Kratochvil, fellow German Florian Mayer was a 7-5, 6-3 winner over Spaniard Albert Portas, while Spain's Felix Mantilla beat Belgium's Christophe Rochus 3-6, 6-2, 6-4.