The fifth-seeded Gael Monfils was upset at the Gerry Weber Open, while second-seeded Dominic Thiem had no difficulties with his opening match.
Thiem defeated German qualifier Maximilian Marterer 7-5 6-3 for a second-round meeting with Robin Haase or David Ferrer.
Monfils lost 3-6 6-4 6-3 to French compatriot Richard Gasquet, who saved 11 of the 13 break points he faced and won in just over two hours despite Monfils' 22 aces to his one.
Spain's Albert Ramos-Vinolas, the eighth seed, was also beaten in the first round of the grasscourt tournament, losing to Russian wildcard Andrey Rublev 6-7 (7-1) 7-5 6-4.
German wildcard Dustin Brown beat Canadian qualifier Vasek Pospisil 6-1 6-7 (3) 7-6 (7-4), and countryman Philipp Kohlschreiber defeated Portugal's Joao Sousa 3-6 6-4 6-4.
Eight-time champion Roger Federer opens his bid for his 16th grasscourt title against Lu Yen-hsun of Taiwan on Tuesday.
Federer was surprised by German veteran Tommy Haas on his return from a two-month break last week in Stuttgart.
The 35-year-old Swiss skipped the claycourt season to recuperate from a busy start to the year that saw him capture his 18th grand slam title at the Australian Open.