Monfils finished off Cilic in five minutes after their match was interrupted by heavy rain Wednesday night.
Next up for Monfils is No. 6 seed Diego Schwartzman. The Frenchman said waiting to play the decisive points against Cilic was very hard.
“We only played four points, but I had to keep my concentration all day long. I am so glad I could do that,” Monfils said.
Cilic won only one match on the clay in Rio in his first tournament since he reached the Australian Open final in January.
Carreno Busta lost last year’s final against Thiem.