Roddick, seeking his first title of the year, defeated Spaniard Alberto Martin, 6-1, 7-6 (7-5) to advance to a meeting with qualifier Philipp Kohlschreiber in the second round of this claycourt event.
Roddick has reached two finals this year, but has not won since last April when he defeated former World No. 1 Pete Sampras in Houston.
"I was happy to close out in straight sets," the 20-year-old Roddick said. "I was close to letting that go and I'm glad I got by. I played a sloppy service game at the beginning of the second set. He hadn't really touched my serve up to that point and I threw in two double faults."
Kohlschreiber, a German ranked 354th in the world, got by Austrian wild card Jurgen Melzer, 6-4, 0-6, 6-2.
Croatian Mario Ancic, who has not reached the quarterfinals in an ATP event, ousted Dent, 2-6, 7-6 (7-3), 6-4, while Dutch wild card Richard Krajicek dispatched fifth-seeded Gambill, 7-5, 3-6, 6-3.
Krajicek's countryman, Martin Verkerk, also registered an upset as he beat Slovakian seventh seed Karol Kucera, 6-2, 6-1.
No. 6 Nikolay Davydenko of Russia avoided an upset as he cruised past Slovakian Karol Beck, 6-4, 6-2.
In other matches, Flavio Saretta rolled to a 6-2, 6-2 triumph over fellow Brazilian Andre Sa; Slovakian Dominik Hrbaty beat Peruvian Luis Horna, 6-3, 7-5; Korean Hyung-Taik Lee defeated American qualifier Hugo Armando, 4-6, 6-4, 6-3; American Brian Vahaly got by Denmark's Kenneth Carlsen, 7-5, 5-7, 6-3; and qualifier Irakli Labadze of Georgia won just his fifth match of the year, a 6-4, 4-6, 6-4 victory over German lucky loser Jan Weinzierl.