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Williams is a 15-time Grand Slam singles champion, and was the No. 3 seed and heavy favorite here, but what made the result all the more surprising was that she has been as dominant of late as she has been in the past: sweeping to the Wimbledon, Olympic and United States Open titles last year and winning 20 straight matches coming into this quarterfinal.

But the streak and Williams's newfound tranquility on court came crashing to a halt on this cool, sunlit afternoon in Rod Laver Arena as Williams, limited and frustrated by a back problem and Stephens's precocious blend of offense and defense, smashed her racket to smithereens early in the third set.

As a result, there will be no rematch between Williams, seeded third, and world No. 1 Victoria Azarenka in the semifinals on Thursday. Instead it will be Azarenka versus Stephens, seeded 29th, who had never been past the fourth round in a Grand Slam tournament until this trip to Australia.

Though she has had other tennis role models besides Williams, including Kim Clijsters, Stephens once had a poster of Williams on her wall.

"This is so crazy, but oh my goodness," Stephens said, wiping away tears in her post-match interview. "I think I'll put a poster of myself now."

It was the first time that Williams, the best player of her generation, had been beaten by a younger American. Williams and Stephens only met recently but they have had considerable contact in the last year.

They were Fed Cup teammates last year and have spent time together in Los Angeles, where Stephens lives with her mother and younger brother and where Williams has a residence.

But they will now be rivals as well as teammates, and this defeat came less than a month after they played for the first time. Williams won that match in the quarterfinals in Brisbane in straight sets, but Stephens was surprisingly comfortable playing at Williams's torrid baseline pace.

Despite the much bigger occasion, she looked comfortable again on Wednesday, handling Williams's power and holding her opening service games before Williams, as expected, closed out the opening set.

Williams then led 2-0 in the second set but Stephens began to lift again. One of the fastest players in women's tennis, she tracked down groundstrokes that would have been winners against most, and managed to break Williams's serve for the first time to get back to 2-all.

But the match took another turn in the eighth game when Williams shouted in pain as she ran forward to get to a short ball. Grimacing, she was quickly broken again as Stephens took a 5-3 lead. Williams, limited in her movement, broke back in the next game and then called for a trainer on the changeover, eventually leaving the court for further treatment on her lower back.

"Well, a few days ago, it just got really tight, and I had no rotation on it," she said. "I just went for this drop shot in the second set, and it just locked up on me. I think I couldn't really rotate after that."

Williams's huge serve was considerably slower after she returned to the court but she still managed to hold at love to 5-all while serving changeups with Stephens visibly rattled. But the teenager fought off a break point in the next game with a forehand winner and then broke Williams for the third time in the set to even the match at one set apiece.

With Stephens up 2-1 in the third set, Williams reared back and smashed her racket twice on the blue hard court, destroying it, and then flinging it at her bench.

"It made me happy, unfortunately," Williams said later.

In earlier times and moods, Azarenka might have been the one to crack at the end of a rough-and-tumble first set full of momentum shifts and grueling rallies. 

But she was simply too consistent, composed and relentless for Svetlana Kuznetsova as she wore down the powerful, experienced Russian and then pulled away, 7-5, 6-1. 

"I'm glad I could produce my good tennis when it was needed," said Azarenka.

Azarenka, a 23-year-old from Belarus who won this title last year, remains the world's No. 1 player, at least for another few days. But her march through the draw has not been as statistically impressive as the likes of Maria Sharapova, who has dropped just nine games in five matches. 

Azarenka was in trouble against the young American Jamie Hampton, dropping a set in the third round and she was in trouble once more early against Kuznetsova, falling behind by 1-4 in the opening set. 

Kuznetsova is ranked just 75th and is still working her way back after a knee injury that spoiled most of her 2012 season. But in an era in which Williams, Azarenka and Sharapova have clearly separated themselves from the pack, the 27-year-old Kuznetsova remains one of the game's most dangerous outsiders: a two-time Grand Slam singles champion with an imposing physique and an unusually well-stocked tennis tool kit that includes — besides the requisite power —  drop shots, sharp angles, crisp backhand slices and that increasingly rare thing, a reliable overhead. 

"I know what kind of tennis she is capable to produce, so I was ready for it," Azarenka said.  "At the beginning, it took a little bit of adjustment because she has such a different game, but I'm glad I could turn around, take control in my hands and really fight through." 

At its best, which was the second half of the first set, this was a terrific match, full of velocity, variety and intensity as both women attacked second serves, solved conundrums posed by the other's strengths and raised both the quality and, yes, the volume.