Nishikori will face defending champion Andy Murray, who carved out a 6-0, 4-6, 7-6 (7/2) win over Steve Johnson of the United States, for a place in the gold medal match.
Monfils had led 4/0 in the final set tiebreaker before his chances disappeared when he double-faulted on his second match point. He was also undone by 51 unforced errors.
Rafael Nadal and Juan Martin del Potro will meet in Saturday's other semi-final.