The big-serving Soderling improved to 2-2 in career matches against Davydenko a quarterfinalist at this year's Australian Open.
Jonas Bjorkman also advanced to the second round after a 6-3, 6-2 win over Daniele Bracciali his second straight career win over the Italian.
In later matches, third-seeded Mario Ancic was playing Andreas Seppi, and fifth-seeded David Ferrer faced Arnaud Clement, reports AP.
Second-ranked Rafael Nadal withdrew from the tournament Monday because of a thigh injury.
"We should use shock therapy to sober up the Americans. In this case, the Americans will speak about the need to resume dialogue. There is no other option"
The United States is concerned about the current crisis in the relations with Russia and suggests returning to reasonable policies to avoid a nuclear war