Being absent from the French tournament through gastroenteritis did not stop Argentine Nalbandian, who beat world number one Roger Federer in last year's Masters Cup final, from securing another trip to Shanghai.
The 2002 Wimbledon runner-up qualified for the year-end event featuring the top eight players in the ATP Race after German Tommy Haas beat American James Blake 6-4, 6-2 in the third round in Paris.
Spaniard Robredo secured a Masters Cup berth by beating local favourite Paul-Henri Mathieu 6-4, 7-6 to advance to the quarter-finals.
Sixth seed Robredo goes on to meet Finn Jarkko Nieminen, seeded 14th, who ended the run of Russian lucky loser Teimuraz Gabashvili with a 4-6, 7-6, 6-2 win.
Nalbandian and Robredo join Federer, Rafael Nadal, Ivan Ljubicic, Andy Roddick and Nikolay Davydenko in the Shanghai field.
Three players -- Blake, Mario Ancic and Haas -- remain in contention for the last spot for the Nov. 12-19 tournament.
On a sad day for the home fans, French number one Richard Gasquet pulled out with an injury in a further blow to the depleted event.
Gasquet, seeded 16th, withdrew before his scheduled third-round match against Russian Marat Safin because of a torn right thigh muscle.
His injury combined with defeats by Mathieu and Julien Benneteau, who was crushed 6-3, 6-1 by ninth seed Ancic, ended French presence in the tournament.
FOURTH TRIUMPH
Former world number one Safin, dreaming of a fourth triumph here after winning in 2000, 2002 and 2004, will now meet Haas.
Ancic faces a tough task in the next round against Davydenko, who stormed through to the last eight with a 6-2, 6-2 demolition of fellow Russian Dmitry Tursunov.
World number five Davydenko is the highest-ranked player in the event after a string of no-shows.
"I'm playing really well and feeling confident but the next match could be tough," said the 25-year-old Russian, who had humiliated Belgian Christophe Rochus 6-0, 6-0 in the previous round.
Defending champion Tomas Berdych, seeded eighth, also advanced easily, beating American Robby Ginepri 6-3, 6-3.
The 21-year-old Czech won the tournament on his first appearance at the Bercy hall last year.
"To have never lost a match here is a nice feeling," he said. "Let's hope it continues".
Berdych's next match will be against Slovakia's Dominik Hrbaty or British number one Andy Murray.
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