"When you're facing a break point, you don't feel like you're going to hope for a mistake," Azarenka said. "You have to make it happen. You have to change the momentum. You have to create something that will surprise her. [She] has the momentum going; she's feeling confident. She has a chance. I had to come up and be strong.
"So I was like, 'OK. Let's do it. If I miss it, I miss it.'"
Azarenka eked out a 6-1, 4-6, 7-6 (5) win in 2 hours, 23 minutes not including an early 76-minute rain delay. She had never lost even a set to the Australian in six previous meetings, but Stosur rallied time and again after a lopsided first set.
"I enjoy the fight," Azarenka said. "I enjoy that struggle, that pain that we go through, that incredible moment that you feel relieved after you gave it all in every point you had."
The rain returned soon after she closed out the win, wreaking havoc on the match that will determine Azarenka's semifinal opponent. Maria Sharapova and Marion Bartoli waited around for more than an hour before starting their quarterfinal, with Bartoli leading 4-0 when the skies opened up again.
The completion of the match was eventually postponed until Wednesday, freeing up Arthur Ashe Stadium for a night session that features a highly anticipated men's fourth-round matchup if the weather clears: Andy Roddick trying to stave off retirement against Juan Martin del Potro.
The rest of the day session was still on, though tournament officials moved around later matches to different courts to try to get play completed with plenty of showers in the forecast.
The seventh-seeded Stosur came back from down a break twice in the third set. She had a chance to go up a break at 5-5 when Azarenka hit that lone ace.
Then in the tiebreaker, Stosur recovered from trailing 4-0.
"There was momentum here, momentum there," Stosur said. "We were hitting winners and running all over the court."
At 5-all in the tiebreaker, Stosur's forehand nicked the net cord and landed short, and Azarenka put the point away with a drop shot.
"I was lucky that the ball caught the net. I was just trying to stay in the moment," Azarenka said. "I didn't really feel like what was the score. I had to do something to surprise, because at this moment you have to come up with something different, not the usual what you do. Because one or two shots will just decide everything."
On match point, Azarenka's final forehand touched down on the baseline, forcing Stosur into a crouch and a wild backhand.
Azarenka improved to 11-0 in three-set matches this year. She had never before made it past the fourth round at the U.S. Open.
The Australian Open champ from Belarus kept Stosur on the run in the first set, breaking her three times. But in the second, Stosur started channeling the aggressive play that allowed her to upset Serena Williams in the final here last year, pounding big forehands for winners.
"I think I'm capable of beating her one day," Stosur said. "Just would have liked it to have been today."
Stosur conceded it had been a "rough" year since she broke through for that first Grand Slam title. She lost in the first round at home at the Australian Open and in her second match at Wimbledon.
But she had the look of a major champion again back here at Flushing Meadows and finally found some answers Tuesday against an opponent who had bedeviled her.
"To really turn it around in one of the biggest tournaments of the year, that's what we come out here and play for," Stosur said. "I think that proves to me that I am capable of doing it. To have another showing here at the Open like this, it for sure gives me confidence to think that maybe one day I can do it again."
The tiebreaker got back on serve after Azarenka double-faulted. She used an expletive later to describe that second serve.
"It was just terrible, terrible," she said. "Wrong movement. I was not focused enough on my execution, what I had to do."
But, Azarenka added, "these kind of mistakes are easier to deal with because they're just silly."
Stosur tied it up with an overhead, but Azarenka was unfazed.
"She really pushed me to dig deep," Azarenka said. "We fought really hard. I felt like there wasn't something (where) somebody was missing. It was always somebody had to grab the opportunity to provoke mistakes. ... The quality of tennis was really high, and it was tense because it could go either way."
P Wednesday, 10 a.m.
TV • ESPN2