However, Williams's relative lack of matches means that her concentration can waver, and whereas she made only two unforced errors in the opener she produced six in the first three games of the second.
That was the first set she had lost against Kanepi of the 10 they'd played to that point, and the first set Williams had lost at the 2018 US Open, a run that included a 6-16-2 victory over her older sister Venus in the third round Friday night.
In the men's singles event, defending champion Rafael Nadal edged past Georgian player Nikoloz Basilashvili 6-3, 6-3, 6-7, 6-4 to book his spot in the last eight.
"I think just like I always say, get your racquet on it, make a play on the ball, make your opponent play an extra ball", Stephens told reporters.
"In the real world, it takes a while for your body to come back".
Kanepi won just six points in the opening set as Williams laid down a marker, but she fought back and used her own ferocious power to blast through the six-time champion.
A year and a day after the birth of her daughter, Alexis Olympia, she was even more dominant in the first set against Kanepi, taking just 18 minutes to inflict a bagel on her opponent.
All the publicity campaigns in the world could not help Serena Williams as she flirted with an abrupt exit from the US Open.
After getting broken in the first game of the second set, Serena fell behind 2-5 before Kanepi served it out on her third set point at 5-4. But after squandering a 2-1 lead in sets, the 11th seed dominated the fifth set to beat 25th-seeded Milos Raonic 3-6, 6-3, 6-4, 3-6, 6-2. It was a crucial moment and the 36-year-old quickly gained an advantage that she never threatened to lose.
Williams took the first set against Kanepi in just 18 minutes.
"It wasn't an easy match at all", Williams said.
Holder Nadal will meet Dominic Thiem for the first time since he beat the Austrian in this year's French Open final. "So I didn't face one break point, and I didn't feel so much pressure on service games". "I think everything is going to happen in time".
Kanepi was responsible for the shock defeat of world number one Simona Halep in the first round in NY and therefore, she looked a potential trouble for Serena, who is still not at her best since making a return after the birth of her daughter.
"And I was just living in this world where I thought it would just automatically come together".
"I know she has a big game, but I have a big game too".