Lindsay Davenport overcame Australia's Alicia Molik 6-4 4-6 9-7 after a titanic struggle on Rod Laver Arena.
Davenport served for the match at 5-4 in the deciding set but urged on by the crowd, Molik saved a match point then converted her sixth break point.
The top seed broke again at 7-7 and after recovering from 15-40 down, she finally sealed her semi-final place.
As she left the Arena, Molik was given a huge ovation by the crowd after a gruelling two-and-a-half hour battle.
Davenport, who goes on to face Nathalie Dechy in the last four on Thursday, was at a loss to explain how she prevailed.
"I am not sure how I am standing here, I feel very lucky to get through that," said the world number one.
"There were a lot of ups and downs. I feel I had it in the third set and let it go and a lot of times you do not get another opportunity.
"It was a really tough match, Alicia is a great player and a great sport."
Molik said her defeat would go on as "one that got away".
"The bottom line is I probably had a chance to win out there," said Molik, who has now lost all four of her meetings with Davenport.
"It's a game of numbers, and I've won 38 out of the last 42 matches, so I can't be too disappointed.
"I gave it my best - it was a battle out there - but she just got me again.
The Australian, playing in her first Grand Slam quarter-final, looked to be on her way out after Davenport wrapped up a routine first set.
Molik was unable to produce the tennis whach saw her oust Venus Williams in the previous round but she was given hope by her opponent.
At 4-5 in the second set, Davenport produced an awful service game, double-faulting twice in a row to hand Molik the set.
After a 10-minute heat break, Davenport rediscovered her serve in the decider and coupled with some crunching groundstrokes, she took control again.
But serving for the match at 5-4, she once again faltered.
Molik saved a match point and squandered five break points before eventually levelling in front of a raucous crowd on Australia Day.
The momentum swung again though and Davenport stepped up the pace to take an 8-7 advantage.
Molik once again fought valiantly to stay in it but Davenport, three times a Grand Slam winner, kept her nerve to advance to the last four.