Nestor's top-seeded team won in 71 minutes on a chilly, grey day at Roland Garros with the threat of rain.
The 39-year-old from Toronto will play for the semifinals against Australian Matthew Ebden and American partner Ryan Harrison.
"We've been playing very solid in these last three matches," said Nestor. "That's quite important. Preparation matches are important but you can't substitute match play for anything.
"No matter how hard you train it's not the same. We've been hitting in the mornings — it's the only time we can get on the showcourts. It's heavier conditions then so we are used to them."
Nestor's team broke three times in victory at an event that the defending champion has won three times with three different partners. He claimed the trophy in 2011 with Mirnyi, the year before with Serb Nenad Zimonjic and in 2007 with Mark Knowles of the Bahamas.
He and Knowles also lost the 2008 final.
Nestor and Minryi were never in trouble against a pair of opponents they beat in an opening match on grass at Queen's Club in London last June.
But Nestor said he and Mirnyi will not be taking Ebden and Harrison for granted.
"They are young guys who are not doubles players but they do well in singles and can translate that to doubles," he said.
"That makes it a challenge to play them. They both hit the ball big, return and serve well. On a slow court, they could be trouble."