Kohlschreiber rebounded after dropping the first set to post a 6-7 (5-7), 7-5, 6-1 win over the 11th-seeded Roddick at the Lindner Family Tennis Center in Cincinnati.
Roddick won the event in 2003 and 2006, and was runner-up in 2005.
Also Monday, No. 12 seed Richard Gasquet of France registered a 6-1, 7-6 (7-4) victory over Ukrainian Alexandr Dolgopolov, while Italian Fabio Fognini scored a 6-4, 6-1 upset victory over 14th-seeded Serb Viktor Troicki.
Other winners on Day 1 included David Nalbandian of Argentina, American qualifier Alex Bogomolov Jr., and Spanish veterans Fernando Verdasco and Feliciano Lopez.
Notable deaths of 2014 [PHOTOS]