Venus told reporters that she never counted the 23-times grand slam champion out of the match.
"I always know that it’s never over until it’s over,” she said. “She kept roaring back, I’m just lucky that I’ve played more matches than her right now.”
Venus, who has climbed to No. 8 in the world after enjoying a strong 2017, had six aces and broke Serena’s service four times, prevailing in a long final game when her younger sister’s groundstroke fell long.
In earlier matches, Australian Open champion Caroline Wozniacki kept alive her hopes of regaining the world number one ranking with a scrappy 6-4 2-6 6-3 third round win over Aliaksandra Sasnovich.
Next up for the 27-year-old Dane, who needs to win the tournament and hope that top seed Simona Halep fails to reach the final, is Daria Kasatkina after the Russian defeated U.S. Open champion Sloane Stephens 6-4 6-3.
Stephens has been in a tailspin since breaking through for last year’s major win, and has failed to advance past a quarter-final this year. Fourth seed Elina Svitolina fell to Carla Suarez Navarro 7-5 6-3.
(Reporting by Jahmal Corner; Editing by Peter Rutherford)
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