Tsonga defeated fellow Frenchman Edouard Roger-Vasselin 6-3, 6-4, and Querrey moved on when wild card Paul-Henri Mathieu retired with a right thigh injury while trailing 6-2.
Querrey broke Mathieu twice and served an ace to take the first set. Querrey will play another Frenchman in the next round, either second-seeded Gilles Simon or Kenny De Schepper.
Tsonga played his first match since a troublesome left knee injury forced him to retire in the second round at Wimbledon and pull out of the U.S. Open. The top-seeded Frenchman, who split with Australian coach Roger Rasheed last month, broke serve once in each set.
Tsonga will meet Tobias Kamke, who rallied from a set and a break down to defeat Hungarian qualifier Marton Fucsovics 1-6, 6-3, 6-2.
Berlocq, who won the Swedish Open in July, did not face any break points in his 6-3, 6-4 victory over Jiri Vesely of the Czech Republic, while Mahut beat Leonardo Mayer of Argentina 7-6 (2), 6-4. Wild card Olivetti defeated 2010 runner-up Mischa Zverev of Germany 7-5, 7-6 (3).
Mahut won two titles in the summer and is enjoying his best season. He blew a 4-2 lead in the first set. But he still won the tiebreaker before breaking Mayer in the opening game of the second set.
Ranked 254th in the world, Olivetti saved four break points in the first set and fired a total of 20 aces.