NEW YORK -- Yes, Serena Williams won in straight sets again. And yes, she moved into an all-American showdown at the U.S. Open against Sloane Stephens. Still, this victory did not quite go according to plan.

Her serve only so-so at times, her footwork a bit off, Williams got by and got through Thursday night against an opponent ranked just 117th, beating Margarita Gasparyan 6-2, 6-4 and letting out a cry of "Yes!" at the end that reverberated in a nearly empty Arthur Ashe Stadium.

It sounded more like relief than excitement.

"The only thing that gets me flustered is really me, like, because I always feel like I'm not winning every point. I mean, like, that doesn't make sense," said Williams, who has won six of her 23 Grand Slam singles titles at Flushing Meadows and was the runner-up the past two years.

"I just think with the pressure and everything that I felt like I just needed to be perfect. I always feel like I'm not perfect unless I'm perfect," she said. "That's not a fun way to live your career and live your life."

Williams, whose older sister, Venus, was one of the few people in the stands, said whatever blips came Thursday "could help me know what not to do next time."

That'll be Saturday against Stephens, the 2017 U.S. Open champion.

It is their seventh matchup; Williams leads 5-1, including victories in the past four meetings, but they last played at the 2015 French Open. Stephens' lone head-to-head victory came all the way back at the 2013 Australian Open.

This caliber of contest certainly doesn't feel as if it belongs in merely the third round at a Slam, but that's the luck of the draw this time.

"I'm playing such a good player so early," Williams said, "so I have to bring what I can even more."

What will also be odd: the quiet.

All spectators were banned from Flushing Meadows this year because of the coronavirus pandemic.

"I know if there were fans it would be so lit, and I'm kind of sad that we're not playing in front of fans, because it would be so fun," said the 26th-seeded Stephens, who advanced by defeating Olga Govortsova 6-2, 6-2. "The atmosphere won't be as big, but obviously a big opportunity to play against the greatest player in the world. So, yeah, unfortunate but still fortunate."

Williams, who turns 39 this month, has won both of her US Open matches in straight sets. But things weren't as easy as they might have been against Gasparyan, who hits flat with a one-handed backhand and whose only trip to the fourth round at a major ended with a loss to Williams at the 2016 Australian Open.

Williams served for the first set at 5-1 and was broken. She went up 4-2 in the second set and was broken, dropped eight of 10 points in one stretch and found herself at 4-all.

In all, she put only 58% of her first serves in and was broken three times.

"I'm just happy to get through it and focus on the next round,'' said Williams, who called a strip of tape on the outside of her left leg "preventative."

In other second-round matches, Tsvetana Pironkova smacked an ace on match point to punctuate a 7-5, 6-3 upset win over No. 10-seeded Garbine Muguruza. This is Pironkova's first tournament after a three-year break to give birth to her son, Alexander.

"If you make a good schedule and have the right motivation, you can combine the two things, motherhood and being a professional tennis player," Pironkova said. "It takes a lot of work, but you know, everything takes work."

A 32-year-old Bulgarian, Pironkova gave birth to Alexander in April 2018. She is playing in her 12th Open but her first since 2016, and it's her first tournament since Wimbledon in 2017.

"It's just great to be playing without that extra pressure I had on myself before," Pironkova said. "Before it was almost like a life-and-death situation for me to win a match. Right now, it's not really like that. It's enjoyment to be on the court."

Pironkova has no ranking because of her layoff.

The win over Muguruza was Pironkova's 22nd against a top-20 player.

"It's not something super new," Pironkova said. "I was moving well and hitting the ball well. Why not win?"

Amanda Anisimova won a faceoff of American teenagers, rallying past wild card Katrina Scott 4-6, 6-4, 6-1. Reigning Australian Open champion Sofia Kenin also advanced, beating unseeded Leylah Fernandez 6-4, 6-3.

Anisimova, 19, a surprise semifinalist at the French Open last year, steadied her game in the second set and pulled away.

Scott, 16, is ranked 637th and was coming off her first tour-level victory in the opening round Tuesday, when she made her debut in the main draw of a Grand Slam. Anisimova, who is seeded 22nd, won the girls' singles at the Open in 2017.

Victoria Azarenka won the battle of the Belarusians by breezing past fifth-seeded Aryna Sabalenka 6-1, 6-3.

Azarenka advanced to the third round in a rematch from last year's loss to Sabalenka at Flushing Meadows. Azarenka, the former world No. 1, reached the U.S. Open final in 2012 and 2013. She's a two-time Australian Open champion.

Azarenka won her first tour title since 2016 last month when Naomi Osaka pulled out of the Western & Southern Open final. Azarenka called her 21st career title special because it's her first as a mother.

She's in the third round of the U.S. Open for the 11th time.

The Associated Press contributed to this report.