Baghdatis, who made the semifinals last week in Marseille, was broken in the 10th game of the third set. Soderling won with a forehand pass as the Cypriot approached the net.
Second-seeded Nikolay Davydenko of Russia defeated Jan Hernych 6-3, 6-3; third-seeded David Ferrer downed Simone Bolelli of Italy 6-4, 7-5; and Michael Llodra of France defeated Raemon Sluiter of the Netherlands 6-1, 7-6 (6).
Nicolas Mahut of France beat Tommy Robredo of Spain 7-5, 6-4. Robredo won two ATP titles last year but has won only one match in an ATP event in 2008, beating Mischa Zverev in the first round of the Australian Open.