Robredo, seeded eighth in the $2.45 million indoor event, was one several players battling in the French capital for the two remaining spots at the Nov 11-18 season-finale in Shanghai featuring the world's top eight.
The winner of the quarterfinal between Briton Andy Murray and Frenchman Richard Gasquet is now certain to knock Robredo off eighth place in the ATP Race.

The unseeded Baghdatis, who stills stands an outside chance of making it to Shanghai, was sharper at crucial moments and sealed victory when Robredo sent a forehand long on the first match point after 86 minutes of play.
The 2006 Australian Open runner-up, in the last four of a Masters Series for the first time, will face either Spain's Rafael Nadal or Russian Mikhail Youzhny for a place in Sunday's final.

"They've just told me I have a chance if Murray or Gasquet don't play the final but I try not think too much about the Masters Cup," Baghdatis said.

Nalbandian prevails
Argentine David Nalbandian, who dropped out of the hunt for tickets to Shanghai on Thursday despite his third-round victory over world number one Roger Federer, advanced to the semifinals but was made to work for it.
The unseeded Nalbandian, who had beaten Federer already in the Madrid Masters final late last month, needed three sets and nearly as many hours to down Spain's David Ferrer 7-6, 6-7, 6-2 in a ferocious contest featuring thrilling rallies.

Fifth seed Ferrer, who has already qualified for Shanghai, matched his opponent's power and determination for two sets but then ran out of steam and Nalbandian wrapped it up with an ace to set-up a semifinal against Murray or Gasquet.

Earlier, Nalbandian became the second man this season to beat  Federer back-to-back with a 6-4, 7-6 (7-3) win in the pre-qaurters, sending the Swiss to the end-of-season Masters Cup on the back of a loss. The Argentine stopped Federer in a Madrid final comeback less than a fortnight ago.

The beefy Argentine, who picked up a coach over the summer and turned his big game on its head, kept the world number one on the hop throughout their third-round contest with a power baseline game on a relatively slow surface on Thursday. After denying the South American the chance to serve out victory leading 5-4 in the second set, Federer then committed errors on three of his last four shots of the match in the ensuing tiebreaker to exit.