Andy Murray, forced to finish a fight in the dark he should have ended with a knockout in the sunlight, drew on all his obduracy to bagel a rampant Gaël Monfils in 21 minutes in the quarter-finals of the French Open and seal one of the most improbable victories of his career.

Beating Monfils 6-4, 6-1, 4-6, 1-6, 6-0 (a scoreline as perverse as the winner) earned him a semi-final against the defending French Open champion, Rafael Nadal, and now all things are possible in the craziest of all possible worlds.

It took Murray three hours and 12 minutes to knock out Monfils but he could have and should have done the job more quickly than the two hours and 34 minutes it took Nadal to beat David Ferrer 4-6, 6-4, 6-0, 6-1 in the other quarter-final on Court Suzanne Lenglen.

Ferrer, one of the game’s renowned fighters, later explained to the media how he lost 13 of the last 14 games. “It wasn’t that good as a match,” he said, “given the players that we are. The court was slow. He started playing a lot better, making fewer mistakes, and I threw in the towel. I don’t usually do this, but I thought, I’m not going to be able to come back. Not against Rafa. He’s such good a player.”

If Murray ever allowed himself such a negative thought, he would probably quit the sport. He laced his own courtside assessment with a good deal of irony when he observed of the man who has won eight titles on Court Philippe Chatrier, “Nadal had good memories on this court. I’ll need to recover well but I’m happy to be in the semi-finals.”

Murray brings a unique ingredient to what will be their 20th encounter, one fashioned from doggedness. In finding the grit to play a fifth set in deteriorating light, Murray was energised. He showed them all: the crowd, who like and admire him but wanted his blood, and his friend on the other side of the net. When a demoralised Monfils drove his final forehand into the net, Murray had pulled off an extraordinary comeback – and he was as sorry for the loser as everyone in France.

“We’ve known each other since we were 10, 11 years old,” he said of Monfils. “I’m very good friends with him, so it’s tough.”

Although he appeared to be pleading with the tournament supervisor Stefan Franzen to let them go to the locker room at two sets apiece, he explained later he was asking how long they might have to play – and he wondered why Franzen was talking only to him, giving the impression to the crowd that it was Murray, and not Monfils, who wanted to stop playing. “I didn’t want to stop the match,” Murray said. “I just wanted clarification.”

Yet, although he was there for the taking, Murray rose from his chair and found what Nadal calls his “inner power” to blow Monfils away. It wasn’t, as he said, “great tennis”, but it was gripping theatre.

Earlier, all was going swimmingly. Murray even felt comfortable to concede the point when a spare ball fell out of his pocket. The hard-headed opinion among the watching pros was that he had been unnecessarily generous – as he was in similar circumstances against Fernando Verdasco. It mattered not. He was soon two sets up. Surely there would be no more surprises. But suddenly Monfils breathed fire at the start of the third. Murray’s serve dipped in the gloaming, the rants to his box grew louder, as did the net. He hit long to give Monfils two set points then netted a backhand to stretch the match into a fourth set.

All the zip was with France’s enigmatic hero and what an hour earlier had been a cakewalk was now a street fight. The match was a rarity at this level in the modern game: a contest between two players without coaches, but it was the Scot who needed a friend the most. Murray has been in a hundred messes such as this and invariably his stubbornness has extricated him but Monfils was performing magic tricks. He held serve more easily and threatened in every shot when receiving. Murray looked leg weary and non-plussed in the face of genius.

Monfils held to love for 4-1 and tapped the most nonchalant reflex volley away for 5-1, before serving out against an opponent whose entire game had collapsed. Murray was on the ropes and ready to go.

Then came the final set, one that no one present will easily forget. The umpteenth turning point in a match that swung violently in all directions went Murray’s way as he smashed a volley to break, then held for 3-0.

Tension gripped the previously rampant racket of the Frenchman as he blasted a forehand long for 4-0. In a twinkling it was 5-0 – and it was Monfils – like Ferrer – who wanted the fight to end. But the deed had to be done. There would be no mercy.

Simona Halep meets Andrea Petkovic in the second of the women’s semi-finals on Thursday after beating Svetlana Kuznetsova and Sara Errani respectively.

Halep, who has charmed fans everywhere with a cheery demeanour to embroider her light-stepping and intelligent tennis, has every chance of going on to contest the title against either the seventh seed Maria Sharapova or the ever-improving Canadian Eugenie Bouchard.

What a year Halep has had. As she waits for her chance to reach her first grand slam final here on Saturday, the 22-year-old Romanian can reflect on a remarkable march through the rankings from No 57, when she went out in the first round at Roland Garros 12 months ago, to No 4 – progress unmatched by anyone in the upper reaches of the game.

Halep had a ruthless 6-2, 6-2 win over the former champion Kuznetsova, who had been in rousing form but was hobbled at the finish as one of her impressive cyclist’s thighs gave up on her. (Her parents and brother were all champion cyclists, and Svetlana gives the stationary bike a very good workout).

Halep is the highest-ranked seed left in the tournament after 11 days of carnage that accounted for Williams along with second seed Li Na and third seed Agnieszka Radwanska.

“It was a perfect game, a perfect day,” Halep said – as was her polite response to a clumsy request to discuss her breast reduction operation of five years ago.

On Court Philippe Chatrier, Petkovic, the former top-tenner who had contemplated retirement after a string of injuries and dropped as low as 177 in the rankings early in 2013, wrapped up her quarter-final against a strangely lethargic Errani 6-2, 6-2, winning 57 points to 36 in the 63 minutes it lasted.