The eighth-seeded Donskoy defeated Khachanov 3-6, 7-6 (4), 6-3.
Sixth-seeded Aljaz Bedene of Britain overcame local wild card Isak Arvidsson 6-4, 7-6 (4) and Argentine Facundo Bagnis beat Jurgen Zopp 6-1, 6-7 (5), 6-1.
Two-time champion David Ferrer and Joao Sousa, who reached the final two years ago, are the top two seeded players this year. Both had first-round byes, along with No. 3 Albert Ramos-Vinolas and No. 4 Marcel Granollers.