Williams, a 21-time Grand Slam winner, suffered just her second loss this year to the 18-year-old Bencic as the oldest and youngest players in the singles draw met in a tense three-set thriller.
Bencic is the youngest player to beat Williams, 33, since she lost to a 17-year-old Maria Sharapova at Wimbledon in 2004.
Bencic has won 20 of her last 24 matches as she beat two top 10 ranked players (Caroline Wozniacki and Ana Ivanovic) to reach the semis.
She advances to Sunday's final, where she will face Simona Halep, who booked her spot with a 6-4, 6-4 win over Italy's Sara Errani earlier in the day.
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