After toppling her older sister in what she called her best match since returning to tennis, Serena Williams ensured Kaia Kanepi, this year's biggest spoiler of the 2018 US Open, would not end her own run toward a title.

Matched up on Sunday with the 44th-ranked Kanepi, who had a historic upset of top-ranked Simona Halep in the first round of the women's tournament, Williams didn't have it easy after a clean first set in which she cruised 6-0. Kanepi, whose earlier victory over Halep marked the first time a top-seeded woman had ever lost in the US Open's first round during the pro era, fought back for a second-set decision to stay in contention and vie for a second straight quarterfinal at Flushing Meadows.

It was Williams, who had 18 aces on the day, who stayed in the spotlight, however, overcoming a seemingly fearless effort from Kanepi to serve her way to victory, a 6-0, 4-6, 6-3 final that sends her to the quarterfinals.

Also in action on Sunday: Defending US Open champs Sloane Stephens and Rafael Nadal, both of whom also advanced.

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. This time around, Basilashvili refused to back down, keeping Nadal on the court at least an hour longer than expected and threatening, even if just temporarily, to derail the ex-Open winner with pure grit. Nadal stepped up at the close, however, to seal a trip to the quarterfinals.

The 25-year-old Stephens, meanwhile, was last but not least on the women's side on Sunday, showcasing smarts and striking in her bout with No. 15 Elise Mertens. Her second-set slam on the move may have been the highlight of the night:

Here's Sunday's full results/schedule:

Men's matches

  • No. 9 Dominic Thiem defeats No. 5 Kevin Anderson 7-5, 6-2, 7-6
  • No. 1 Rafael Nadal defeats Nikoloz Basilashvili 6-3, 6-3, 6-7, 6-4
  • No. 11 John Isner defeats No. 25 Milos Raonic 3-6, 6-3, 6-4, 3-6, 6-2
  • No. 3 Juan Martin del Potro vs. No. 20 Borna Coric, 9 p.m.

Women's matches

  • No. 8 Karolina Pliskova defeats No. 18 Ashleigh Barty 6-4, 6-4 
  • No. 17 Serena Williams defeats Kaia Kanepi 6-0, 4-6, 6-3 
  • No. 19 Anastasija Sevastova defeats No. 7 Elina Svitolina 6-3, 1-6, 6-0
  • No. 3 Sloane Stephens defeats No. 15 Elise Mertens 6-3, 6-3