Russell, the 34-year-old former University of Miami player ranked 83rd in the world, has never won a singles title in ATP Tour play. Paire, a 23-year-old Frenchman, was slowed by an abdominal muscle strain.
"It was extremely difficult," said Russell, the oldest player in the field. "Benoit has a really awkward game style. You never know what to expect, a winner, a drop shot, an ace, a double fault. He really gets you out of your rhythm. I just tried to dig deep and luckily I got through it. I was pretty proud of myself mentally."
There were nine service breaks in the first set, five by Russell, before Paire dumped a forehand into the net on the fourth set point. In the second set, Russell broke for a 4-3 lead, rallied from 15-40 down to hold for a 5-3 lead, and won on the fourth match point when Paire put a backhand return into the net.
In other second-round matches, fourth-seeded Nicolas Mahut beat Paolo Lorenzi 7-5, 7-6 (7), fifth-seeded Xavier Malisse held off Matthew Ebden 6-4, 6-3, and Ricardas Berankis beat Igor Andreev 6-4, 7-5.
Mahut will play Berankis, and Malisse will face second-seeded Sam Querrey, the 2009 and 2010 tournament winner who missed the event last year after undergoing surgery for a right shoulder injury.
"I'll try to put as many returns (as possible) in play, that's the first thing," the 32-year-old Malisse said. "But I think I've just got to go out and look at my own game. Try to concentrate on what I'm doing, keep trying to hit serves like that and be aggressive.
"I feel like I played a lot more aggressive than in the first round. I have to stick to that. I'm going to miss some shots, but I think eventually it's paying off. It's better for me to play that way."