"It was funny to play a younger player out there for once," said Roddick, 20, who ranked sixth in the world. "He broke early to go up 2-1, but then I really picked up my game, I thought. I served better than him. He sprayed some balls."
Kohlschreiber came into the tournament ranked 354th in the world.
"I had a great week this week qualifying and winning my first tour match," the teen-ager said. "The difference between me and Andy is that he plays the top guys in every match. I only get to play top players so often."
Play was suspended because of rain on Tuesday after only one match was completed, forcing No. 2 seed Albert Costa of Spain to double up on Wednesday.
Costa completed a 6-7 (4-7), 6-1, 6-3 first-round victory over Serbia's Nemad Zimonjic, but he was not as fortunate in the night session, suffering a 6-4, 2-6, 6-2 second-round loss to rance's Anthony Dupuis.
Costa, who is preparing his title defense at next week's French Open, went just 7-5 on clay this spring.
Former Wimbledon champion Richard Krajicek of the Netherlands reached the quarterfinals with a 6-2, 2-6, 6-3 victory over American Brian Vahaly.
"Didn't expect anything coming into this tournament," Krajicek said. "I just came here to get some practice for the grass court season. Any win that I get is a bonus. My condition is great and I'm feeling good."
Two other seeds reached the round of eight. No. 6 Nikolay Davydenko of Russia ousted Hyung-Taik Lee of Korea, 6-4, 6-3, and No. 8 David Sanchez of Spain bounced Italian Davide Sanguinetti, 6-4, 6-4.
In other matches involving unseeded players, Martin Verkerk of the Netherlands got past Slovakia's Dominik Hrbaty, 6-4, 7-5; Mario Ancic of Croatia toppled Jean-Rene Lisnard of France, 6-4, 7-5; and Brazil's Flavio Saretta advanced with a 6-1, 6-1 rout of Georgian qualifier Irakli Labadze.