Mayer took out Martin Fischer 6-2, 6-2 in 58 minutes, winning 60 percent of the points in the match. He finished off all five of his break opportunities and won more than half -- 27-of-47 -- of the points off Fischer's serve.
Mikhail Youzhny earned a second-round match against fourth-seeded Kei Nishikori with a 6-1 6-2 romp over Daniel Gimeno-Traver in a rapid 48 minutes. Youzhny lost only eight points on serve -- an 80 percent win rate -- and took 56 percent of the points when Gimeno-Traver served.
Also Monday, Jan Hernych, a qualifier, picked up his first ATP main-draw win of the year with a 6-4, 6-2 decision over Daniel Brands. Hernych faced only two break points and converted five of his eight break chances.
Mischa Zverev topped David Goffin 1-6, 6-4, 7-5. Goffin, due to the lopsided first set, won more points in the match (102-99) but Zverev dropped serve just once of the final two sets to advance.
World No. 3 Roger Federer, who has won the Gerry Weber Open five times and was runner-up in 2010 and 2012, is the No. 1 seed for the tournament, with Richard Gasquet second and defending champion Tommy Haas seeded fourth. The top four seeds received first-round byes.
Federer and Haas also played together as a doubles team but were beaten Monday by Jurgen Melzer and Philipp Petzschner 7-6 (7-3), 6-4.