Baghdatis breezed past Igor Andreev 6-2, 6-4 in a second round match at the Connecticut Tennis Center in New Haven, Conn.
Other early-round matches Tuesday saw Lukas Lacko of Slovenia upsetting No. 2 seed Thomaz Bellucci of Brazil 6-4, 6-7 (4-7), 6-0, and Radek Stepanek of the Czech Republic upending third-seeded Fernando Gonzalez 6-2, 6-4.
No. 5 seed Andrey Golubev of Kazakhstan brought down Argentine Maximo Gonzalez 6-3, 2-6, 6-2 and eighth-seeded German Florian Mayer handled Czech Jan Hajek 6-3, 6-1.
American Taylor Dent was dispatched by sixth-seeded Spaniard Tommy Robredo 5-7, 6-4, 6-4 in a night match.