The No. 16-seeded Monfils became soaked with sweat on a sweltering afternoon but rallied from a 4-1 deficit in the final set. Nishikori fell behind 0-40 serving at 4-5 but erased those match points and another in that game, and overcame one more match point serving in the 12th game.
"I thought I almost gave up the match,'' Nishikori said. "It was tough conditions. Especially the last couple of games, I don't know what I was thinking.''
He played a solid tiebreaker and closed out the victory with a forehand winner.
The Associated Press contributed to this report.