Contrasting fortunes for sisters
The world No 1 recovered from being a set and a double break behind to overpower her rival 4-6 7-6 (7/4) 6-2 and book her place in the semi-finals.
Hopes of an all-Williams match-up in the last-four were dashed after Venus was on the opposite end of an equally impressive comeback from China's Li Na.
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Hide AdVenus had the chance to serve for the match in the second set but was made to pay as she lost a marathon match with the 16th seed 2-6 7-6 (7/4) 7-5 in two hours and 47 minutes.
Serena followed her sister onto court in the second match of the day, and admitted she thought she was heading out of the tournament after some aggressive hitting from Azarenka had the seventh seed from Belarus on the brink of an upset.
Azarenka was 4-0 ahead in the second set and four-time winner Williams revealed: "I wasn't feeling great at that stage.
"I was actually thinking 'If I lose today and I lose in doubles I think I can catch a flight on Friday'. That's not what a champion is supposed to think, but that's what I was thinking. I'm just happy to still be here."
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Hide AdLi's victory means China will have two players in the semi-finals of a major for the first time after Zheng Jie won through to play Justine Henin in the bottom half of the draw.
Britain's Laura Robson moved into the quarter-finals of the girls' event with a 6-3 6-3 win over Cristina Dinu.