The fourth-ranked Briton next plays the winner of the quarterfinal match between Roger Federer and Juan Martin del Potro, who defeated defending champion David Nalbandian on Thursday.
Monfils made a good start at the Madrid Arena by breaking Murray's serve in the opening game, but the U.S. Open finalist broke back immediately to even the match on the indoor hard court.
Both players held their serves until Murray broke Monfils to go 4-2 up. Murray broke again to take the first set.
The second set followed the same pattern, with Monfils becoming erratic in his returns.
"He almost enjoys running too much and almost likes you to dictate play,'' Murray said of his 22-year-old opponent. "Once he get used to big matches we're going to be seeing a lot more of him.''
Murray admitted losing concentration during some points, making him shoot long.
"It could have been a comfortable match but for that,'' Murray said.
Murray was relaxed about the possibility of meeting Federer, who beat him 6-2, 7-5, 6-2 in the final of the U.S. Open.
"I'm not feeling under pressure to win every match,'' Murray said.
Del Potro knocks Nalbandian out at Madrid
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