The American dropped a set for the first time in the tournament as Kanepi - a two-time quarter-finalist in these parts - bounced back from a horrific start.
Six-time former champion Serena Williams will continue her quest for a seventh US Open title against the last woman to beat her in New York, Karolina Pliskova.
Stephens, fresh from an impressive victory over the hard-hitting Victoria Azarenka, takes on 15th seed Elise Mertens of Belgium, who beat the American third seed in straight sets at the Western and Southern Open in Cincinnati last month. Last night, another potential foe, the Wimbledon champion Angelique Kerber, was facing Dominika Cibulkova in her attempt to join Williams in the fourth round. I worked really hard on that instead of trying to hit a trick shot or do fancy stuff.
Supreme Court nominee Brett Kavanaugh's lips sealed on White House subpoenas, pardons
He likened it to another controversial, landmark Supreme Court decision, the Miranda ruling about the rights of criminal suspects. Judge Kavanaugh had dissented when, in 2011, his court upheld new restrictions on assault weapons in the District of Columbia.
Serena Williams defeated her sister Venus 6-1 6-2 to reach the US Open fourth round. She then started strongly against Kaia Kanepi only to face a spirited fightback from the Estonian, but Williams eventually prevailed 6-0 4-6 6-3. A couple of loose points gifted Kanepi a break in the first game of the second set, however, and she couldn't get back on terms.
So what if it happened to be her big sister?
It has been suggested that a 24th slam title would mean more to Williams now that she is a mother, yet she insists it would have been impossible for her motivation to increase.
That was all she needed as 18 aces and 47 total winners proved plenty to put her through.
Chicago Bears: 10 bold predictions following Khalil Mack trade
Carr took a bit less to get Jackson done and keep the Raiders on schedule to extend Mack the following offseason. "We all knew. Gruden addressed the trade Sunday, and he made things a whole lot more confusing while explaining why the deal happened .
A lot has to happen if a rematch against Williams - which was due to happen at the French Open before injury intervened - is to happen, but Sharapova is the only Grand Slam victor left in the bottom half.
Kanepi is ranked only 44th, but she's been a top-20 player in the past and has made it to Grand Slam quarterfinals a halfdozen times.
There will be another rematch in the last eight between defending champion Sloane Stephens and Latvia's Anastasija Sevastova. "We always have tough matches, so I am just happy to get through".
The 17th-seeded Williams has seen Pliskova before at the U.S. Open, falling to the Czech player 2-6, 6-7 in the 2016 semifinals. "So I didn't face one break point, and I didn't feel so much pressure on service games". "I don't think my desire to win could have been more five years ago or today".
Airstrikes hit last bastion of Syrian rebels as final showdown looms
The meeting will also discuss how to coordinate on continuing the political process and the counter-terrorism in Syria, he added. Since then, hundreds of thousands of people are believed to have been killed and millions more displaced by the conflict.
"I hope it's going to be on Ashe", said Sevastova. I have watched her a great deal since then. So I have some weapons, too.