The 31-year-old Davydenko, now 42nd-ranked after peaking at No. 3, saved Wawrinka's five breakpoint chances in a second set that went with serve.
Wawrinka, ranked 17th, faltered in the tiebreaker, dropping three points on serve for Davydenko to win in two hours, 14 minutes.
Sixth-seeded Mikhail Youzhny was another Russian winner, easing past Bernard Tomic of Australia 6-0, 6-2.
Grigor Dimitrov of Bulgaria upset eighth-seeded Viktor Troicki of Serbia 6-3, 6-2.
In other matches, Brian Baker of the United States beat Radek Stepanek of the Czech Republic 2-6, 7-6 (5), 6-3, and Matthew Ebden of Australia beat Victor Hanescu of Romania 6-3, 7-6 (3).
Marco Chiudinelli of Switzerland joined childhood friend Roger Federer in the second round, beating Spain's Guillermo Garcia-Lopez 5-7, 6-3, 6-4. Kevin Anderson of South Africa downed Jarkko Nieminen of Finland 7-6 (4), 6-3.
Federer plays his first match on Wednesday.
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