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Fifth seed Bencic came from a set down to beat 167th-ranked German Niemeier 4-6 6-4 7-5 in Berlin on Monday.
The 21-year-old Niemeier was playing her first professional match on grass and gave a great account of herself against the world number 12, who needed two hours and 12 minutes to secure her place in the second round.
Bencic secured the only breaks in the second and third set to ensure she will face Petra Martic or Asia Muhammad in round two.
Madison Keys progressed in straight sets, getting the better of Polish qualifier Magdalena Frech 6-3 6-4.
The American, a winner of two WTA singles titles on grass, struck 19 winners as she set up an encounter with top seed Aryna Sabalenka.
There were also first-round victories for Alize Cornet and Ekaterina Alexandrova earlier in the day over Amanda Anisimova and Anna Kalinskaya respectively.