The Briton overcame injury and a one-set deficit to eventually defeat Finland's Jarkko Nieminen.
Top seed Novak Djokovic overcame his troublesome ankle problem to see off Finland's Jarkko Nieminen 6-4 6-3.
The Swiss maestro beat unseeded Finn Jarkko Nieminen 6-3 6-4 to successfully defend his hometown title in Basle.
In the second round, home hope Florian Mayer upset third seed Jarkko Nieminen, beating the Finn 6-4 3-6 6-4.
Australia's Bernard Tomic also reached the last four, with the 20-year-old beating veteran Finn Jarkko Nieminen 6-7 (6-8) 6-4 6-2.
Second seed Juan Martin del Potro cruised into the semifinals with a victory in straight sets against Finland's Jarkko Nieminen.
He will now play Jarkko Nieminen in the last eight after the Finn beat German qualifier Matthias Bachinger 6-3 5-7 6-3.
Andy Murray continued his quest for an Olympic singles medal by beating Finland's Jarkko Nieminen to reach the third round at Wimbledon.
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Meanwhile Russian Nikolay Davydenko defeated Jose Acasuso from Argentina 6-4 6-3 while the fourth-seeded Russian Marat Safin beat Jarkko Nieminen from Finland 6-3 6-3.
Second seed Gonzalez, seventh in the Masters Cup race, overcame Croatian qualifier Roko Karanusic 6-4 7-6 to set up a meeting with unseeded Finn Jarkko Nieminen.
The 25-year-old pulled out of the recent Rome Masters with a back injury but showed no signs of discomfort as he set up a second round clash with Finland's Jarkko Nieminen.
Tsonga overcame Finland's Jarkko Nieminen 7-6 6-4 6-3 to set up a clash with compatriot Jeremy Chardy, while Monfils battled past Latvia's Ernests Gulbis 6-7 6-4 7-6 6-2 to earn a third round tie with Tommy Robredo.
Japan's Kei Nishikori reached the last eight thanks to a 6-3 6-3 win over Spain's Tommy Robredo, while Alexandr Dolgopolov of Ukraine progressed when Finland's Jarkko Nieminen retired due to a migraine with the Ukrainian ahead 6-2 4-1.
Murray had been accused of being a "drama queen" by former tennis star Virginia Wade after receiving lengthy on-court treatment during an earlier match against Jarkko Nieminen, but revealed he had refused pain-killing injections to counter the back pain he has been suffering since the start of this year.
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