Need the scores from any match played in this or any other tournament? Results
Robredo beat Jeremy Chardy 7-6 (4), 7-6 (5) and Tursunov defeated Adrian Mannarino 6-3, 6-2. Robredo saved the only break point he faced in the first set, while Tursunov broke Mannarino's serve five times.
Tursunov next plays third-seeded Novak Djokovic, while Robredo faces No. 15 Fernando Verdasco.
Last year, Richard Gasquet jumped from 13th to eighth and took the final spot for the Masters Cup by reaching the semifinals in Paris.
Gasquet pulled out on Sunday because of an injury to his right elbow.
"I felt the injury during the Madrid (Masters) tournament," he said. "Of course I am very disappointed."
Roddick dented his chances of reaching Shanghai after losing to Robin Soderling in the quarterfinals of the Lyon Grand Prix on Friday. Simon picked up points there by reaching the semis, and Roddick could play Simon in the third round in Paris.
Top-ranked Rafael Nadal, 13-time Grand Slam champion Roger Federer, Djokovic, Andy Murray and Nikolay Davydenko have already clinched their spots for Shanghai, but Davydenko is the only one among them to have won the Paris tournament, in 2006.
Nadal will hope to go one better than last year, when he was beaten 6-4, 6-0 by David Nalbandian in the final, while Federer will be hoping to put an end to his Paris jinx by reaching at least the semifinals for the first time.
Nadal, who already leads the ATP for titles this year, will go for his ninth trophy of the year.
The Spaniard could meet Frenchman Gael Monfils in the third round and Davydenko in the quarters, while Federer would open against either Josselin Ouanna or Robin Soderling -- against whom he is 7-0.