Haase was down after the first set but battled back for a 4-6, 6-1, 6-4 decision over Mayer to gain the second round at Autotron Rosmalen.
Also notching a victory Sunday was German Daniel Brands, who dispatched Jesse Huta Galung of the Netherlands 6-3, 6-2.
The two-time defending champion at the Dutch Wimbledon tuneup is David Ferrer of Spain.
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