By Theo Ruizenaar
World number six Davydenko dropped his first service game but regained control to take the opening set into a tie-break.
However, Soderling who had never won a tie-break against the Russian in 10 previous meetings, prevailed and a break in the ninth game of the second set was enough to give him the match.
The 25-year-old Swede had started the year with first-round exits in Chennai and the Australian Open.
"I came here with hardly any confidence after my start of the season and had no idea what to expect this week, but that improved after every round just like my performances" Soderling told reporters.
"Today was my best performance so far and every match is still getting better."
(Editing by Clare Fallon)