Having come through one epic encounter with Philipp Kohlschreiber - 12-10 in the final set - in the third round, Murray saw off Monfils 6-4, 6-1, 4-6, 1-6, 6-0 in a match every bit as up and down as the score suggests.
"I was just lucky in the end that he started the fifth set badly," said Murray, after equalling his best result at Roland Garros.
Murray and Monfils played a five-set match on Court Philippe Chatrier eight years ago, a match that the Frenchman won.
The Wimbledon champion was in total control after dominating the first two sets only for the Frenchman to galvanise the crowd by roaring back to force a decider.
But the Scot proved the stronger in the final set and came through to set up a semi-final against eight-times champion Rafael Nadal.
"It was really tricky conditions at the start, very windy," he said. "But I started well. Then when the wind calmed down he started playing so much better; he's such a great athlete, the best we have, and some of the shots he chased down were incredible. I was just lucky in the end."
Murray admitted he was glad to have closed out the match as darkness fell. "I didn't want to stop either. It was 20 past nine," he said. "I was told we had 20 minutes left so, you could potentially play two or three games in that time. Six was the maximum. I mean, it was so dark at the end."
As for facing Nadal, who recovered from a set down to beat fellow Spaniard David Ferrer in four sets, Murray acknowledged everything will need to fall his way if he is to make it to the final for the first time. "He's got some good memories on this court," Murray said, smiling. "But I'm very happy to be in the semi-finals and now I will have to make sure I recover well to be ready for that match."