Starace, seeded fifth, landed 81 percent of his first serves and lost only 10 points on serve in a 7-5, 6-2 win over Daniel Brands. Starace faced one break point in 10 service games.
The seventh-seeded Fognini was pushed to a third set before escaping a challenge from Gerard Granollers-Pujol 6-2, 4-6, 6-3. Fognini had five aces but also 10 double faults. However, he converted seven break-point chances.
Filippo Volandri was a 7-5, 6-3 victor over Julien Benneteau while Ruben Ramirez-Hidalgo topped Rui Machado 7-5, 6-1 and Federico Gil beat Simone Bolelli 6-3, 6-1 in other first-round matches.
Also moving into the second round were Michael Berrer, who swept past Nicolas Devilder 6-3, 6-3, and Andrey Kuznetsov, who beat fellow qualifier Sergio Gutierrez-Ferrol 6-1, 7-6 (7-5). Blaz Kavcic advanced when Reda El Amrani, who was leading 4-3, retired because of injury.