The 19th seed, who is playing his first Grand Slam tournament since Wimbledon last year after struggling with a wrist injury, outlasted his opponent in a topsy-turvy battle.
The 28-year-old finally got the better of world number 51 Paire in a dramatic fifth set which saw three consecutive breaks of serve before Nishikori saved four break points to serve it out.
“It was a very difficult match, he played a really good second and third sets,” he said.
“I changed some things and played good in the last two sets.”
The former US Open finalist, who has reached the last eight twice in Paris, will next face Frenchman Gilles Simon who put out American 12th seed Sam Querrey for a place in the second week.