Nadal, who saved five match points before taming Nicolas Almagro in another all-Spanish battle on Wednesday, needed two hours and 20 minutes to shrug off a brave challenge from Robredo, seeded 14th in the indoor event.
"I didn't play my best but I played better than yesterday and managed to play big rallies without making mistakes, so that's positive," Nadal said.
Robredo had his chances, serving for the match in the third set, leading 5-4, but Nadal lived up to his reputation as a fierce competitor to recover and seal victory.
Roger Federer's second-round exit in the French capital on Wednesday means Nadal stands an outside chance of finishing the year as world number one.
Before contemplating that accolade he must beat defending Paris Masters champion Jo-Wilfried Tsonga, the world number nine, who swept aside fellow Frenchman Gilles Simon 6-2, 6-3.
"The conditions will be good for him with a fast court and the crowd on his side," Nadal said. "He will be the favourite but I'll do my best."
TIRED MURRAY
France will have two players in the quarter-finals for the first time since 1992 after 15th seed Gael Monfils posted a 6-4, 6-3 win over Julien Benneteau, who looked exhausted after his shock victory over Federer in the previous round.
Britain's world number four Andy Murray looked tired, too, when he lost 1-6, 6-3, 6-4 to Czech Radek Stepanek.
Despite having battled for over two hours to beat James Blake on Wednesday, finishing in the middle of the night, Murray started well against Stepanek, relying on his strong serve, but then collapsed, making many unforced errors.
"Obviously, I was not at my best but I was not expecting to (be)," Murray told reporters. "It was four o'clock by the time I got to bed and that's not the ideal preparation for a match."
Stepanek now faces US Open champion Juan Martin del Potro, who moved past Chile's Fernando Gonzalez in dramatic, late action.
Gonzalez won the first set 7-6 and world number five Del Potro had just won the second by the same score after surviving seven match points when the Chilean pulled out with a sore right knee.
Murray will now rest before going to London where he could meet Swede Robin Soderling, who kept alive his slim hopes of entering the year-end event by beating Russia's Nikolay Davydenko 6-3, 3-6, 6-4.
Soderling goes on to meet world number three Novak Djokovic, who cruised past Frenchman Arnaud Clement 6-2, 6-2 to reach the quarter-finals in Paris for the first time.
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