The Russian will face seventh seed Marat Safin, who beat Julien Benneteau of France 6-4 6-0 6-2.
Meanwhile at the World Tennis Tournament in Rotterdam, Juan Martin del Potro will face Julien Benneteau in Sunday's final.
Gilles Simon advanced, and so did Julien Benneteau, despite losing 10 straight games during one stretch of his second-round match.
Verdasco breezed past Frenchman Julien Benneteau 6-2 6-1 in just under 75 minutes, while Tsonga defeated Nicolas Almagro of Spain 7-6 (7-5) 7-5.
Michael Llodra and Julien Benneteau beat Fernando Verdasco and Feliciano Lopez 6-1 6-2 6-7 (6-8) 7-6 (7-5) to give France an unassailable 3-0 lead.
Federer will play home favorite Julien Benneteau in the next round after the Frenchman prevailed 7-6 7-5 5-7 0-6 6-4 against Germany's Tobias Kamke.
Fifth seed Mardy Fish maintained the form he showed last week by moving into the second round with a comfortable win over Julien Benneteau.
Meanwhile, defending champion Roger Federer crashed out of the Rotterdam World Tennis tournament after suffering a shock 6-3 7-5 defeat by France's Julien Benneteau.
Also advancing were No. 22 Fernando Verdasco, No. 28 Marcos Baghdatis, the 2006 Australian Open runner-up, No. 31 Radek Stepanek and No. 32 Julien Benneteau.
Julien Benneteau of France upset Dominik Hrbaty of Slovakia 7-6 (2) 5-7 6-1 and Thailand's Paradorn Srichaphan was also ousted in the second round, falling to Belgium's Xavier Malisse 7-6 (7-3) 6-3.
The U.S., who are without Andy Roddick or Mardy Fish, will look to the Bryan brothers (Bob and Mike) to edge them into the lead tomorrow as they face Michael Llodra and Julien Benneteau.
In the remaining second-round matches to be completed, Julien Benneteau won 6-0 in the fifth set to edge past Colombia's Alejandro Falla, while Florent Serra needed four tight sets to eliminate Romania's Victor Hanescu.
Harrison chalked up his first ever win over an opponent ranked inside the world's top 15 with his 6-4 6-4 success against Isner on Wednesday, but he lost his quarterfinal match 6-4 6-2 to Frenchman Julien Benneteau.
Latvia's Gulbis, seeded 24th, lost in straight sets to Jeremy Chardy , 28th seed Radek Stepanek lost 6-4 6-2 4-6 6-4 to Julien Benneteau and 30th seed Juan Monaco was sent packing by Canada's Peter Polansky in straight sets.
Wimbledon's closed roof made for a fascinating atmosphere on Centre Court later in the day, but Federer was already showered and changed and thinking of a third round meeting with France's Julien Benneteau -- who beat American Michael Russell -- as he bids to equal Pete Sampras' record of seven Wimbledon titles.
CNN: Federer thrashes Fognini to reach round three at Wimbledon
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