Russell, ranked 83rd in the world, dropped Paire 7-5, 6-4.
The other seeded players in Thursday's action were all victorious. No. 4 seed Nicolas Mahut of France dropped Italian Paolo Lorenzi 7-5, 7-6 (9-7), fifth seed Xavier Malisse of Belgium beat Matthew Ebden of Australia 6-4, 6-3, and sixth seed Marinko Matosevic of Australia eliminated Tobias Kamke of Germany 6-3, 1-6, 6-0.
Richard Berankis of Lithuania beat Russian Igor Andreev 6-4, 7-5.