The sixth-seeded Kohlschreiber held his serve throughout and broke Struff once in the first set and again in the final set.
''I was the better player in the rallies but his serve made it a close match,'' said Kohlschreiber, who reached the final here in 2012 but failed to win his opening match the following two years.
Andreas Haider-Maurer came back from a break down in both sets to beat Joao Souza of Brazil 7-6 (2), 6-4 and set up a second-round match against fellow Austrian Dominic Thiem.
The 21st-ranked Thiem, who is coming off back-to-back titles in Umag and Gstaad, is the top-seeded player at the final clay-court event of the season after David Goffin of Belgium pulled out for personal reasons.
Another Austrian, Jurgen Melzer, also advanced by defeating Daniel Gimeno-Traver of Spain 7-6 (3), 6-3. The former eighth-ranked Melzer, who entered on a wild card, next plays Nicolas Almagro of Spain.
Almagro hit 20 aces while rallying to beat the seventh-seeded Jiri Vesely of Czech Republic 6-7 (2), 7-5, 6-4.
Also, Albert Montanes of Spain beat Gerald Melzer, Jurgen's younger brother, 6-4, 7-6 (5), and Dusan Lajovic of Serbia defeated Mikhail Youzhny of Russia 6-3, 6-4.