He beat Germany's Nicolas Kiefer 4-6, 3-6, 6-4, 6-1, 6-2 to set the enviable record of being the first player to fight back from two sets down three times in a Grand Slam event.
The Frenchman, ranked just 81st in the world, also came back from the brink against Sweden's Magnus Larsson in the first round and the experienced American Richey Reneberg in the third round.
Escude, who had beaten the 12th seed and French Open champion, Gustavo Kuerten, in the second round, won a match lasting 2hr 27min that was packed with incident.
Kiefer needed treatment on an injured ankle in the fourth set and the match was also held up for more than 30 minutes by a downpour of rain. "I can't say it's a great feeling," said Kiefer, ranked 29 in the world and the German No 1 now that Boris Becker has gone into semi-retirement. "I had a lot of chances to win the match and I'm very disappointed. It was a great chance to get into the semi-final."
Escude is now on track to become a new French tennis "musketeer''. If the 21-year-old beats ninth seed Marcelo Rios in the semi-final, he will be the first Frenchman to reach the Australian Open final since the legendary Jean Borotra won the title in 1928.
Borotra was one of the four ``musketeers'' - with Lacoste, Cochet and Brugnon - who dominated the sport in the 1920s.
The Chilean Rios booked his match with Escude by rallying to beat the Spaniard Alberto Berasategui 6-7 6-4 6-4 6-0. Rios' victory ended the run of Berasategui, who beat the second seed, Patrick Rafter, and ended Andre Agassi's comeback campaign.
But the Chilean admitted he was very close to leaving the Czech Petr Korda as the only seed still in the men's competition as increasing leg cramps slowed his game. The Chilean told his opponent when they shook hands at the end of the 2hr 34min match that he could not have gone into a fifth set.
"At 5-0 I felt some pain in my leg and thought a fifth set would have been really tough," Rios said. He is now the only player to have reached at least the fourth round at the last five Grand Slam tournaments.
In the women's singles Martina Hingis marched on towards a second Australian Open title by sweeping aside France's Mary Pierce, her opponent in last year's final, to reach the last four.
Hingis beat Pierce 6-2, 6-3 to set up a semi-final with the 10th seed Anke Huber, who recorded a surprise 7-6, 7-5 win over Spain's Arantxa Sanchez Vicario. "I just played very well from the start," Hingis said. "She just made so many unforced errors. I don't know what happened to her."
Hingis, who won three of the four Grand Slam tournaments last year including the Australian Open, had been nervous going into the match because she was beaten by Pierce the last time they met in New York in November. Pierce still leads 4-3 in their career head-to-head, but Hingis is clearly in the ascendancy now.
The Swiss added: "I didn't need to play my best today. I didn't need to play that many winners - she just missed so many balls."
While Pierce hit everything out of court or into the net, Hingis again stepped up her game. In each set Pierce and Hingis dropped their opening service games, but the teenager regained her composure first.
The French fifth seed said: "I think I played the worst match of the tournament and unfortunately it was today. I wasn't moving enough. My legs just weren't there, my serve wasn't there and that's why I made so many unforced errors."
Hingis expects a tougher challenge from Huber, the German runner-up to Monica Seles in 1996.
Huber said of her victory: "I played from the start the way I wanted to play, was patient and waited for my chances." Her only problem was some frustration in the second set when a series of double-faults hampered her ability to close out the match at 5-4.Reuse content