Six-time champ Serena battles into US Open quarter-finals

Williams, the 23-time Grand Slam champion seeking a first major since a 2017 Australian Open title won when she was pregnant with her daughter Olympia, will take on Karolina Pliskova for a semi-final spot after the eighth-seeded Czech beat Australian Ashleigh Barty 6-4, 6-4.

Williams looked set for a romp when she seized the first set from Kanepi in just 18 minutes.

But the hard-hitting Estonian, who took out world number one Simona Halep in the first round, settled down in the second, boosted by an opening break as she took a 2-0 lead.

After a Williams double fault gave Kanepi a break for a 5-2 Williams answered by winning the next two games.

But she couldn't convert two break chances in the 10th, and after Williams saved two set points Kanepi knotted the match with a service winner on her third set point.

“It wasn’t an easy match at all," said Williams, who let out a roar after ripping a backhand cross court to hold serve in the oepning game of the third set.

"She's had a lot of big wins in her career. I was just happy to get through it to be honest."

Williams took control of the final set with a break for a 2-0 lead, her 18 aces and 47 total winners proving enough in the end to put her through.

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.

She can also avoid her first year since 2011 without a Grand Slam title. She missed her Australian Open title defense, not returning to the tour until March.

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.