Russell will be trying to reach the first ATP final of his career when he meets Mahut Saturday.
In the second of the day's two quarterfinal matches, Russell surprised No. 3 seed Igor Sijsling 7-6 (7-3), 6-7 (6-8), 7-6 (7-5). Russell is ranked 95th in the world.
Mahut, who was the runner-up in this tournament six years ago, defeated Michael Przysiezny 7-6 (7-5), 6-4.
The other quarterfinals will be contested on Friday with two-time defending champion John Isner taking on Ivo Karlovic and Lleyton Hewitt facing Jan Hernych. Isner defeated Hewitt in last year's final.
The Hall of Fame tournament is the ATP Tour's only grass court event played in the United States.