Williams, the fifth seed, lost her concentration after a bizarre incident at break-point and 2-0 down in the second set. Some of the trademark beads from her hair sprayed over her side of the court and the American was deducted a point.
The Swedish umpire, Denis Overberg, docked her the point and she lost the game under a new WTA ruling brought into existence when the Williams sisters started playing with their beaded hair.
"This is not a disturbance. Nobody's causing a disturbance. This has never happened to me before," Williams told the umpire. She appealed to the referee, Peter Bellenger, but he supported the umpire and Williams screamed in anguish as she turned on her heels to play the next game. But she never recovered her composure, and Davenport romped through.
"The first time it happened the umpire looked at her and said if it happens again you lose the point. Maybe she should have argued the first time," said Davenport, the world No 1 and top seed in Melbourne. "It's unfortunate, but the umpire played by the rules."
She said she deliberately went out to test Williams. "I played really solid tennis and tried to force errors. I kept the ball deep and then went for my shots. I did everything I wanted to do," she said.
Davenport also believes Williams needs to improve her all-round game. "She goes for her shots and if it doesn't work she doesn't have a plan B to fall back on," she added. "I think today she just collapsed. She's got to be a little tougher in these kind of situations. She just lost her composure. If you have got a player off their game you try and keep them there, which is what I did."
Williams said: "I don't think it was a very fair call. I've never had such treatment before from any other umpire at any other match. I don't think it's a real distraction."
Mauresmo, the world No 29, beat the 11th seed, Dominique Van Roost of Belgium, 6-3, 7-6. The Belgian was constantly on the back foot, pinned to the baseline by Mauresmo's big forehand.
It is not the first time the 19-year-old Mauresmo has battled through to the latter stages of a tournament as an outsider. She beat Davenport - whom she next meets in the semi-final - and the Wimbledon champion, Jana Novotna, to reach the final in Berlin last May as a qualifier.
Swede Thomas Enqvist emerged as favourite to win the men's singles after reaching his first Grand Slam semi-final by beating the unseeded Swiss player Marc Rosset in straight sets. Enqvist, also unseeded, won 6-3, 6-4, 6-4 in 1hr 41min against the man who beat Tim Henman in the third round.
The Swede's sensational run of form has seen him eliminate Australia's two leading players, the US Open champion, Pat Rafter, and the 14th seed, Mark Philippoussis. In the last three weeks he has won the Australian Hardcourt Championship, his three matches at the Kooyong Classic exhibition and his five matches here.
It was the 24-year-old's fourth successive win over the big-serving Rosset, who let himself down with his erratic forehand and was foot-faulted seven times, six of them in the opening set.
Enqvist will now play Nicolas Lapentti of Ecuador - a distant 91st in the world rankings - who battled to a five-set win over the seventh seed, Karol Kucera of Slovakia.
The unseeded Lapentti, who had failed to progress beyond the second round of his 11 previous Grand Slam appearances, beat Kucera 7-6, 6-7, 6-2, 0-6, 8-6 to reach the semi-finals.
Earlier, in the girls' singles, Britain's Hannah Collin was the first winner of the ninth day. She moved through to the second round by cruising through her opening match with the loss of only two games. Collin defeated the Australian Melissa Dowse 6-1, 6-1.
Another British player, Lee Childs, bowed out when he lost his boys' singles second-round match against the 12th seed Joachim Johansson, the Swede prevailing 7-6, 6-3.Reuse content