The result left Serena Williams 11-0 in three-set matches this year.
Serena Williams said of her older sister, "She's the toughest player I ever played in my life, and the best person I know, so it's going against your best friend and going against, for me, the greatest competitor in women's tennis."
Next up for Serena Williams is a semifinal match against unseeded Roberta Vinci. The Italian advanced by beating another unseeded player, Kristina Mladenovic of France, 6-3, 5-7, 6-4.
Mladenovic struggled with cramps during the match, which was played during the hot afternoon conditions.
This is the farthest Vinci has advanced in a Grand Slam singles event. Her previous best efforts came in the 2012 and 2013 U.S. Opens, when she advanced to the quarterfinals. She lost in the first round at both the French Open and Wimbledon this year.
On the men's side, defending champion Marin Cilic advanced to the semifinals, but he was stretched to the limit.
The ninth-seeded Cilic, of Croatia, won his 12th consecutive U.S. Open match by beating 19th-seeded Jo-Wilfried Tsonga of France 6-4, 6-4, 3-6, 6-7 (3), 6-4 in a match that took nearly four hours.
The length of that match delayed the start of the featured match of the day between the Williams sisters.