The 26-year-old Paradorn, ranked 51, ripped 45 winners in his victory over the Russian, who had reached the semi-finals at the French Open and the last eight at the Australian Open.
The Thai will next face Italian David Sanguinetti, who also vanquished a seeded player in number 31 Carlos Moya, the 1998 French Open champion.
Sanguinetti beat Moya 3-6, 6-1, 6-2, 6-4.
