Williams could meet defending champion Sloane Stephens in the semifinals should she overcome eighth seed Karolina Pliskova in the last eight.
"I think every athlete, every human and definitely every African-American should be completely grateful and honored", Williams told The Associated Press.
After Kanepi broke early to go up 2-0 in the second, a rare double-fault by Williams handed the Estonian a break and a 5-2 lead. Plus, it's worth remembering this- Kanepi eliminated No. 1 Simona Halep on Day 1 of this tournament.
Williams heads into the second week at Flushing Meadows tracking two milestones: A seventh US Open title would see her break out of a tie with Chris Evert for the Open Era record and also equal Australian Margaret Court's all-time record of 24 major titles.
Nadal faced Georgia's Nikoloz Basilashvili, the 2018 German Open contender and one of his opponents at Roland Garros in 2017, when the former had a relatively smooth path to victory - a 6-0, 6-1, 6-0 win.
Sen. James Inhofe: McCain Is 'Partially to Blame' for Flag-Raising Controversy
McCain, who died at age 81 on Saturday after battling brain cancer, was an avid sports fan and supporter of Arizona's teams. "Sen. The church service brought to a close two days of mourning for the six-term senator and presidential nominee in his home state.
Facing Pliskova, who reached the quarterfinals with a 6-4, 6-4 victory over Ash Barty on Sunday, should provide Williams a good measure of where she stands. She withdrew prior to a fourth-round meeting with Maria Sharapova at the French Open with a shoulder injury before a scintillating run to the Wimbledon final ended with a runner-up finish to Angelique Kerber.
"She got there for a reason, she has a lot of strong parts to her game", Williams said.
The actress, 33, put on a loved-up display with her beau, as he leaned over to give her a kiss on the cheek as they watched the action unfold on the court at the Billie Jean King National Tennis Center. In the third, however, the American regrouped and pounded a great return that earned a wide response and brought her 2-0 up. "I'm going to continue to grind and see what happens". I'm only in my third one back. She was bumped up to the No. 17 seed at the U.S. Open. I think it makes it unnatural.
It certainly was. And that chase-down, turn-around, hook-shot of a passing victor showed a glimpse of how the No. 3 Stephens can go from defense to offense with flair, as she did repeatedly during her 6-3, 6-3 victory over No. 15 Elise Mertens of Belgium in the fourth round. "Wouldn't you love to see one of these National Football League owners, when somebody disrespects our flag, to say, 'Get that son of a bitch off the field right now. Out!"
"I feel like it's important for women to know that it doesn't happen like in that Instagram world".