The fifth-seeded Spaniard finished with 19 aces, earning the only break of the match in the third game of the opening set. He then jumped out to a 5-1 lead in the second-set tiebreaker.
The seventh-seeded Kohlschreiber broke serve twice in each set to defeat Olivier Rochus of Belgium 6-1, 6-4.
French qualifier Maxime Teixeira saved 11 break points, but still lost 6-3, 3-6, 6-4 to the eighth-seeded Nieminen, who won the Sydney International this month.
Cipolla rallied past Marc Gicquel of France 1-6, 6-4, 7-5. Russell topped Adrian Mannarino of France 6-3, 7-5, and Mathieu beat Cedrik-Marcel Stebe of Germany 6-4, 6-4 to earn his first victory this year after missing the 2011 season because of a knee injury.