Grand Slam champions Iga Swiatek and Ashleigh Barty survived challenging opponents on Thursday to make their way into the third round of the US Open.

No.7 seed Swiatek of Poland was in great peril before she overcame Fiona Ferro of France, 3-6, 7-6(3), 6-0 in just over two hours of topsy-turvy play.

2020 Roland Garros champion Swiatek fended off the threat from World No.74 Ferro to reach the US Open third round for the second straight season.

Stat box: Swiatek improved to 2-0 against Ferro, as she had beaten the Frenchwoman at the last hardcourt major, in the third round of the 2021 Australian Open. But that encounter was a breezy straight-set win for Swiatek, while this match was anything but.

The first set had Ferro in control, with eight winners to just five unforced errors, while Swiatek's 11 winners in the opener were outweighed by 15 unforced errors. But Swiatek cleaned up her act as she methodically steered her way back to victory, finishing the match with 37 winners to 35 unforced errors.

Turning points: The close first set took a turn in Ferro's direction when Swiatek double faulted to drop serve and cede a 5-3 lead to Ferro. Earlier in the set, Swiatek broke back immediately after Ferro took a lead, but this time was different, as Ferro pulled a string of return errors from the Pole to hold at love.

Sturdier forehands by Swiatek helped her claw back from a quick break down and lead 4-2 in the second set, but Ferro continued to fight, using powerful forehands of her own to pull back on serve at 4-3. The Frenchwoman stared down two set points at 6-5, but she came out on top in increasingly lengthy rallies to hold serve, queuing up a tiebreak.

With her back against the wall, though, Swiatek showed off her mettle. A stunning inside-out forehand down the line gave the Pole a 5-2 lead in the breaker, and she eased home from there, drawing a handful of long errors from Ferro to clinch the second set.

Swiatek had no problems racing through the third set to claim the comeback win.

Swiatek says: "For sure, it was a tough match," the No.7 seed told the media, after her comeback. "I think I didn't start it properly, because I felt like I couldn't properly feel my legs. But it's not the first time, so I'm trying to work on that. In the second set, I loosened up a little bit, kind of changed tactics."

Next for Iga: Another tough battle likely awaits Swiatek in the third round. She will face No.28 seed Anett Kontaveit of Estonia, last week's champion in Cleveland.

Kontaveit powered through a difficult second-round draw of her own on Thursday, dispatching this month's Montreal finalist Jil Teichmann of Switzerland, 6-4, 6-1. Kontaveit was never broken in her 70-minute victory over the rising World No.44 Swiss.

As for World No.1 Barty of Australia, she staved off a late challenge by 18-year-old Clara Tauson of Denmark, 6-1, 7-5, to book her spot in the third round of the 2021 US Open.

After her hour-and-a-half victory over World No.78 Tauson on Arthur Ashe Stadium, reigning Wimbledon champion Barty is now into the third round for the fourth time in her last four appearances in New York. Barty, though, is still seeking her first trip to the US Open quarterfinals or better.

Stat corner: Barty's 33 winners well outpaced Tauson's total of 14, and the teenager was also undone by 25 unforced errors during just the second US Open main-draw match of her career.

Barty broke serve five times in the affair, and was solid with her first serve, firing 11 aces and winning 80 percent of her first-service points in total.

Key moments: An incredible second game went Barty's way, but not without a struggle, as the Aussie needed 10 break points in that game before she could take the Tauson serve and open up a 2-0 lead. From there, though, Barty had no trouble sweeping to the one-set lead.

Tauson's power game, though, helped her to put up a terrific fight in the second set. After falling behind an early break, Tauson broke Barty for the first time to tie up the set at 1-1, then held on for 5-4 with some clutch serves, saving a match point in the process.

Barty served for the match in the next game, but some excellent play at the net by Tauson, coupled with Barty miscues, allowed the Dane to pull level at 5-5. But Barty got back ahead with another break for 6-5, and though she had to save one more break point in that game as well, the top seed held on for the win.

Words from the No.1: "Today was tricky, I think, to navigate through that second set and just trust myself and hit out," Barty said in her post-match press conference.

"Being able to respond straightaway was a big part of that match," Barty added. "Just refocusing, and narrowing my focus, and remembering what I needed to do to win the match as opposed to getting flat and passive, where I was letting her control a little bit too much."

Next up: Barty will face 2020 US Open quarterfinalist Shelby Rogers of the United States in her next match. There are no seeded players remaining in Barty's potential path to a first US Open quarterfinal.

Kerber exacts revenge on Kalinina

2016 US Open champion Angelique Kerber of Germany needed to wait an extra day to get her second-round match off the ground, as the terrible weather conditions on Wednesday night made playing her match untenable.

But No.16 seed Kerber shook off the changes with ease, as the former World No.1 zipped past Anhelina Kalinina of Ukraine, 6-3, 6-2, in just over an hour, to reach the third round in New York for the ninth time in her career. This week marks Kerber's 48th consecutive Grand Slam event.

Kerber grabbed a measure of revenge over World No.76 Kalinina, as the Ukrainian had knocked her out in the first round of Roland Garros earlier this year. This time around, the three-time major champion had all the answers, with 23 winners to just 14 unforced errors, and a break point conversion rate of 5-of-6.

"I played good today, I think," said Kerber. "I knew [she is] always a tough opponent. I lost against her in Paris this year, so I was prepared what to expect. I was focusing from the first point. I think that I was really aggressive today, and I think that was the key for me, for the match today."

Kerber raced to a 4-0 lead in an unorthodox way: she saved break points in both of her service games, and Kalinina could not win a point in either of hers. After getting on the board, Kalinina edged closer in the opener, but the German's forehand worked when it had to, and she fired a winner from that wing down the line to take the first set.

Kerber then cruised through the second set to clinch the victory, lining up a third-round match against an opponent she has had trouble with: 2017 US Open champion Sloane Stephens of the United States. Stephens has won five of their six previous meetings.

"We played so many matches," Kerber said, looking ahead to Stephens. "She's always a tricky opponent. She can play everything. I know that here, especially here, she is always playing her best tennis. I have to be ready from the first point."

Kvitova, Pavlyuchenkova fight their way into round 3

No.10 seed Petra Kvitova entered the US Open third round for the 11th time in her career as she ousted fellow Czech lefty Kristyna Pliskova, 7-6(4), 6-2 in an hour and 18 minutes on Louis Armstrong Stadium.

115th-ranked Pliskova, who successfully braved the qualifying this year, upset Kvitova in their most recent encounter at 2018 Charleston. But two-time Wimbledon champion Kvitova moved through this time after a difficult first set with no service breaks, improving to 2-1 over the twin sister of World No.4 Karolina Pliskova.

"I knew it would be a tough one, especially when she's serving really big, which she did, actually," Kvitova said in her post-match press conference. "I'm glad that I was able to win the tiebreak, for sure. That was the key for the whole match afterwards."

Another tough test awaits Kvitova in the third round: No.17 seed Maria Sakkari of Greece.

This year's Roland Garros finalist Anastasia Pavlyuchenkova also earned a tough victory, as the No.14 seed from Russia outlasted Slovakian qualifier Anna Karolina Schmiedlova, 6-2, 5-7, 6-2 in over two-and-a-half grueling hours of play.

Pavlyuchenkova had 27 winners to former Top 25 player Schmiedlova's 17, as the Russian keeps her hopes alive for a second trip to the US Open quarterfinals -- 10 years after she made it to that round in 2011. She will next face fellow Russian Varvara Gracheva for a spot in the round of 16.