Robredo has reached the French Open quarterfinals four times before, but never gone farther.
Robredo beat John Isner 6-7 6-3 7-6 after Sanchez saw off American Melanie Oudin 6-4 6-4.
There are comebacks, there are shocks, and then there is Tommy Robredo at this year's French Open.
Nadal faces Philipp Petzschner on Thursday after the German eliminated Spanish 15th seed Tommy Robredo 7-6, 7-6.
Fish beat Tim Henman and Tommy Robredo at the Madrid Masters last week before losing to Roger Federer.
Spaniard Robredo, the fifth seed, lost 1-6 6-3 6-2 to 10th seed Tomas Berdych of the Czech Republic.
The Serbian opens his account on Tuesday against Sergiy Stakhovsky of Ukraine, and could meet Robredo in the quarterfinals.
The Gold Group features Rafael Nadal, Nikolay Davydenko, Tommy Robredo and James Blake, all of whom begin their campaign on Monday.
In Tuesday's only second round match, Wimbledon runner-up Tomas Berdych overcame a stomach problem to see off Spain's Tommy Robredo 6-0 6-4.
The other winners on Tuesday were Tommy Robredo of Spain, German duo Bjorn Phau and Michael Berrer, and Somdev Devvarman of India.
Robredo, 30, had not won a title since triumphing at Santiago in February 2011, but will now return to the top 50 following his success.
Federer, world number two and defending champion, was given a scare by Tommy Robredo before stumbling through 6-3 3-6 6-3 6-2 after 40 unforced errors.
The Australian Open semifinalist beat compatriot Tommy Robredo 6-3 6-2 on Saturday, while Stanislas Wawrinka beat yet another Spaniard in Nicolas Almagro, winning 6-3 7-5.
Sweden's Robin Soderling, a French Open finalist, dropped the first set of his opening match before eventually seeing off Tommy Robredo of Spain 4-6 6-1 6-4.
Spain's seventh seed Tommy Robredo lost to Argentine Jose Acasuso 2-6 6-3 6-4, and Croatian fourth seed Ivan Ljubicic beat France's Arnaud Clement 7-6 (8-6) 6-4.
In Sunday's action in the Hopman Cup , Tommy Robredo and Maria Jose Martinez Sanchez gave Spain a 3-0 win over the United States in Perth.
Fifth seed Tommy Robredo also progressed with a 7-6 (7-4) 6-4 win over Dutch wildcard Robin Haase, and the Spanish world No. 15 will next play Florian Mayer.
Tommy Robredo and Feliciano Lopez beat Jonathan Erlich and Andy Ram 7-6 6-7 6-4 6-2 to put Cup holders Spain 3-0 up against Israel in the best-of-five tie.
The host nation needed to win all three rubbers in straight sets to snatch a final spot off the unbeaten Spanish pairing of Maria Jose Martinez Sanchez and Tommy Robredo.
Meanwhile, Spain's Tommy Robredo claimed his first title in two years after defeating South Africa's Kevin Anderson 7-6 4-6 6-3 in the final of the Grand Prix Hassan II in Morocco.
Fourth seed David Ferrer defeated Italian Potito Starace 4-6, 7-5, 6-2 in what he called "a very physical match" and 2004 champion Tommy Robredo overhauled Russian Igor Andreev 4-6, 6-2, 6-3.
Earlier Federer survived a loss of form in a scrappy second set before finally coming through in four sets against Robredo, world number 52 and a quarter-finalist in this tournament four years ago.
Hewitt joined another former world No. 1 in progressing as Juan Carlos Ferrero upset seventh-seeded Spanish Davis Cup teammate Tommy Robredo 6-3 6-2 to set up a clash with German 10th seed Tommy Haas.
Spain won the Hopman Cup for the third time, beating Great Britain 2-1 in the final in Australia as world No. 4 Murray was upset by 16th-ranked Tommy Robredo in the men's singles rubber.
Other players left sitting it out were third seed Tomas Berdych of the Czech Republic, who was due to play home hope Tommy Robredo, fifth seed Milos Raonic of Canada and Japan's sixth seed Kei Nishikori.
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.
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