Former champions Agnieszka Radwanska (2011) and Jelena Jankovic (2008) won their second-round matches, but two-time former winner Svetlana Kuznetsova lost to Andrea Petkovic of Germany 4-6, 6-4, 6-1.
Slovenian qualifier Polona Hercog ousted Ana Ivanovic 6-4, 6-4 and will play Radwanska for a spot in the last eight.
Nadal and Kohlschreiber traded five breaks of serve in their first set but couldn't break the other in the second and were separated only in the tiebreaker. Nadal won for the 11th time in 12 matches with the German.
Also, Fabio Fognini of Italy, enjoying his career-best year with two titles, routed Lleyton Hewitt 6-0, 6-2, and eighth-seeded John Isner also advanced.