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With her trademark combination of aggression and consistency, Azarenka gave Williams all kinds of trouble for the first half of the match, taking the first set, 6-3, then breaking early en route to leads of 3-1 and 4-2 in the second. It looked like Williams' 16-match Grand Slam winning streak was about to end.
The No.1-seeded Williams rifled one last forehand to beat the No.27-seeded Azarenka, 3-6, 6-4, 6-2.
"I was really disappointed with my last match, and I knew I couldn't play like that against someone like Vika. It would be impossible to win," Williams said. "Even though I lost the first set, I told myself, 'Well at least you're playing better than in your second round match.' I would have lost so easily if I played that same way. It was definitely better today - it's definitely a step in the right direction.
"And I just really want to be here."
"The level of the match was pretty high quality from both players, and she really stepped it up," Azarenka said. "She went for a lot of shots that landed right on the line, and she really just stayed aggressive. Looking back at it, I've got to learn from that and maybe stay a little bit more aggressive and go a little bit more for my shots too. But there wasn't much wrong that I've done, I don't think.
"She just played a good match and I have to give her credit for that."
With the win, Williams becomes the first woman in the Open Era to win 50 matches at all four Grand Slams - not even Chris Evert, Martina Navratilova or Steffi Graf achieved that milestone (more here).
The World No.1 was told the stat in her post-match press conference and seemed to be in disbelief.
"Yeah, I don't understand that, because it's just weird to me," she said. "I was thinking, 'Are you sure Martina didn't do it, or Chrissie Evert?' Yeah, that's just strange. But I feel really good about it."
Awaiting Williams in the fourth round will be WTA Rising Star Sloane Stephens, who won eight of nine games from 4-all in the first set to get past Tsvetana Pironkova in an hour and 15 minutes, 6-4, 6-1.
Williams leads Stephens in their head-to-head, 4-1, and won their only clay court meeting, too - in fact that came just a few weeks ago at the Mutua Madrid Open (watch highlights from the match here).