Giannessi, No. 183 in the world, qualified for his first main draw of the year Monday and came back with a 7-5, 6-4 victory over Montanes. Giannessi saved seven of the 10 break-point situations he faced and cashed in five service breaks in 11 receiving games.
No. 7-seeded Andreas Seppi claimed a 6-1, 4-6, 6-1 decision over Eric Prodon in the other match Tuesday involving a seeded player. Seppi won half the points off Prodon's serve and finished with six breaks in 12 games.
Igor Andreev joined Seppi as the only three-set winners Tuesday, defeating Peter Torebko 5-7, 7-4, 7-5. Torebko fired off 12 aces but lost his serve five times.
In other first-round matches, Florent Serra beat Gianluca Naso 6-2, 6-4; Marius Copil topped Victor Crivoi 6-3, 6-3 in an all-Romanian matchup; Adrian Ungur got past Lukas Rosol 6-4, 6-1; Filippo Volandri eliminated Rui Machado 6-3, 6-3; and Albert Ramon took a 6-4, 6-3 decision over Victor Hanescu.