Delbonis won 7-5, 7-6 (2) against Bellucci who also took the clay-court title at Swiss ski resort Gstaad in 2009. Delbonis will continue rising in the rankings after victory over Federer in the Hamburg semifinals helped him climb from No. 114 to 65.
Federer is top-seeded this week and has a second-round match scheduled on Thursday, against Daniel Brands of Germany who took a set off him in the second round at Hamburg.
Brands advanced from the first round Tuesday by beating Marco Chiudinelli, Federer's Swiss childhood friend, 6-3, 3-6, 6-2.
Eighth-seeded Roberto Bautista eased past Henri Laaksonen, 6-2, 6-3; Daniel Gimeno-Traver beat Kenny De Schepper, 6-4, 6-4; Guillermo Garcia-Lopez beat Adrian Ungur, 6-4, 6-7 (2), 6-1; and Pablo Andujar eliminated Victor Crivoi, 6-1, 6-2.
Victor Hanescu beat qualifier Dustin Brown 7-6 (6), 6-2.
Robin Haase beat Joao Souza 6-4, 7-6 (7), and will next face third-seeded Janko Tipsarevic.