Victor Hanescu also advanced when Dmitry Tursunov retired with a strained left thigh muscle trailing 6-4, 6-6 (3).
Russia's Dmitry Tursunov also fell victim to home talent as Philipp Kohlschreiber knocked out the event's sixth seed 6-4 7-6 (8-6).
He will next face 31-year-old French qualifier Sebastien De Chaunac, who later upset No. 14 seed Dmitry Tursunov of Russia 3-6 7-6 (7-3) 7-5.
Mario Ancic and Ivan Ljubicic beat Dmitry Tursunov and Igor Andreev 6-2 4-6 7-6 3-6 6-4 to give Croatia a 2-1 lead against Russia.
Del Potro outclassed World No.97 Daniel Brands 6-4 6-2 while Berdych overpowered Russian wild card Dmitry Tursunov 6-3 6-2 in just over an hour.
Kvitova's compatriot Berdych beat Russian qualifier Dmitry Tursunov 6-2 6-1, while Tsonga was similarly dominant as he defeated fellow Frenchman Gilles Simon 6-2 6-2.
Novak Djokovic reached the third round when Dmitry Tursunov withdrew from their match because of a shoulder injury, when he was trailing 6-2 4-3.
Baker went down 6-1 6-3 to in-form American Mardy Fish in his first ATP Tour event and Bogdanovic lost 7-6 6-4 to experienced Russian Dmitry Tursunov.
But his top billing proved to be a curse as the world No. 4 crashed out 7-5 3-6 6-1 in the second round to Russian Dmitry Tursunov.
The Scot must win the tournament to keep alive his slim hopes of qualifying for the Masters Cup and will meet fifth seed Dmitry Tursunov in the last eight.
And on a good day for Russia, Igor Andreev beat Gael Monfils 7-5 6-4 and Dmitry Tursunov reached the third round after Nicolas Almagro retired when trailing 6-3 5-4.
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That leaves their fate in the hands of world number six Nikolay Davydenko, 20th-ranked Igor Andreev, Dmitry Tursunov (26) and Igor Kunitsyn, who is ranked 76 in the world.
Serbian ninth seed Janko Tipsarevic lost the opening set to Russia's Dmitry Tursunov, but scrapped to claim a 5-7 7-6 (14-12) 6-3 6-4 success and a place in round two against Australia's 20-year-old debutant James Duckworth.
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