Nishikori won 6-2, 6-7 (8/10), 6-2, 6-7 (8/10), 7-5 in a shade under four hours to reach his third last-eight clash at the French Open.
"He almost had it today," said Nishikori who had led two sets to one when the last-16 tie was suspended on Sunday.
"He served for the match at 5-3 but I just tried to fight and play one point at a time."
The 29-year-old Japanese could have wrapped it up in the fourth set when he had two match points but he squandered both, the second on a double fault.
Paire, the world number 38 who was trying to make the quarter-final of a Slam for the first time, was eventually undone by 15 double faults and 79 unforced errors.
Nishikori has only defeated 11-time French Open champion Nadal twice in 12 meetings with both of those wins coming on hard court.
The 33-year-old Spaniard has won all four of their meetings on clay.
"It's going to be a tough match, he's the greatest ever clay court player," said Nishikori.
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