Six-time champion Serena Williams survived a spirited challenge from unseeded Kaia Kanepi to triumph 6-0, 4-6, 6-3 on Sunday and reach the quarter-finals of the US Open. The 23-time Grand Slam champion looked set to romp home when she seized the first set from Kanepi in just 18 minutes, but the hard-hitting Estonian, who took out World No. 1 Simona Halep in the first round, settled down in the second set, shaking off the partisan crowd in a jammed Arthur Ashe Stadium to push Williams the rest of the way.

"It wasn't an easy match at all," said Williams. "It was a big relief for me to win a big game and a very important one," she added. Defending champion Sloane Stephens, the third seed, eased past Elise Mertens 6-3, 6-3 to book a quarter-final rematch with Latvian Anastasija Sevastova. Sevastova toppled seventh-seeded Elina Svitolina 6-3, 1-6, 6-0, leaving just two of the top 10 women's seeds remaining.