Nestor and Zimonjic reached the quarter-finals of the Grand Slam tournament on Saturday with a 6-4, 7-5 victory over 13th seeds Jean-Julien Rojer of the Netherlands and Romania's Horia Tecau.
"The best thing we're doing is playing very consistent," said Nestor. "When we are down or in tough situations, we don't get emotional, this is our strength right now.
The victory in just under 90 minutes puts the third seeds up against the winner from Austrian Jurgen Melzer and Spain's Feliciano Lopez versus Croatia's Marin Draganja and Florin Mergea of Romania. That match is scheduled for Sunday.
"It still one match at a time," said Nestor. "If we play the way we have, we have as good a chance as anyone to win the tournament."
Tecau proved to be the weak link on Saturday, with the Romanian losing serve once per set as Nestor and Zimonjic won their 11th consecutive match on clay.
The pair came to Paris with trophies in Madrid and Rome; Nestor has won the French doubles title four times since 2007.
Tecau was broken in the ninth game of the first set and in the penultimate game of the second, with the 41-year-old Nestor from Toronto serving out the win and Zimonjic clinching victory with a poached cross-court winner.
"We're playing well for sure, but there's been a lot of luck involved," said Nestor. "We've won a lot of close matches and hit some lucky shots. But we're on a roll and that's what happens sometimes."