NEW YORK -- When Jessica Pegula lost the first two games of the second set to Petra Kvitova, it looked like the two-time major champion was on the verge of another comeback. Kvitova saved two match points in the third round against Garbiñe Muguruza and seemed to be trending in the same direction.

“I just told myself not to get frustrated,” the No.8-seeded Pegula said later. “I wanted to stay committed to hitting my spots and was able to work my way back.”

She was too modest. Pegula won six straight games Monday to defeat Kvitova for the first time, 6-3, 6-2.

Pegula will next play No.1 Iga Swiatek, who came back to beat Jule Niemeier 2-6, 6-4, 6-0.

Here are three thoughts on what Pegula and Swiatek need to do to continue their success in New York:

Iga Swiatek

Seek a good return on investments

One of the constants in Swiatek’s rise this year has been an uncanny ability to break opponent’s serves. Her athleticism and anticipation are the biggest reasons.

In her fourth-round victory against Niemeier, she managed it seven of 13 times. She’s an unworldly 21-for-37 at the US Open. The yearlong record, going back to 2008 when the statistic was instituted, belongs to Victoria Azarenka, who in 2013 won return games an astonishing 54.8 percent of the time.

Swiatek, who has been flirting with that number for much of the season, currently leads all players with 52.6 percent.

Manage the nerves

Swiatek sailed through her first four matches, winning all eight sets, but came a bit unglued in the opening set against Niemeier. She screamed in the general direction of her box, and gave its occupants a sarcastic thumbs up when she double-faulted away a service game. At the lowest point, she slammed her towel back into its bin with a snarl.

“I’m just proud that I didn’t lose hope,” Swiatek said in her on-court interview. “I had a hard time pushing her back. I’m pretty glad it worked.”

Doubtless there’s more angst ahead when she meets Pegula for the third time this year. Keeping it all together should be Goal No.1.

Forget those Paris memories

Pegula and Swiatek have played three times, with Swiatek taking both matches in 2022.

She prevailed in the Miami semifinals, 6-2, 7-5 -- in a match that was more tightly contested than the score might suggest -- and the quarterfinals at Roland Garros 6-3, 6-2. That was on clay, of course, and Pegula is a better player on hard courts,

“She’s really consistent,” Swiatek said of Pegula. “She’s a great player. I know it’s going to be tough. We’re going to analyze for sure the previous matches. I think she has a game style that suits these courts.”

This one looks like a fair fight; both players are into their third major quarterfinal of the year. No other player left in the women’s draw can say that.

Jessica Pegula

Keep working through the distractions

After breaking Kvitova to open the match, there was an eight-minute delay when rain visited Arthur Ashe Stadium. After Kvitova broke back and played three points on her serve, the rain returned. This time it required 45 minutes to close the roof and mop up the mess.

Pegula left the court, did some stretching, and never lost her composure. She came out focused and methodically went to work on Kvitova. The placid look on her face during changeovers is the window to her poise in a turbulent environment.

Kvitova, it should be mentioned, had won her past two matches against Top 10 players -- after having lost nine of the previous 10.

Continue that consistency

Pegula finished the 2020 season ranked No.63, but broke through at the 2021 Australian Open, reaching the first major quarterfinal of her career. It was hardly a fluke.

This year, she’s reached the quarters in three of the four Grand Slam tournaments, in Melbourne, Paris and now New York. That’s vaulted her into the Top 10 for the first time back in June -- and she’s held her position nicely. Pegula reached the semifinals in Toronto, losing to eventual champion Simona Halep, and the quarters in Cincy, again falling to the eventual winner, Caroline Garcia.

At this US Open, Pegula has been going along nicely, dropping only one set, that coming in the third round against qualifier Yuan Yue.

Look forward, not back

With her victory over Kvitova, Pegula altered her history this fortnight.

She had lost both previous matches to Kvitova, including a third-rounder at the 2020 US Open -- both in straight sets.

Moreover, she had lost all three previous matches against seeds at the Billie Jean King National Tennis Center, to No.11 Belinda Bencic (2021), No.6 Kvitova (2020) and No.4 Agnieszka Radwanska (2016).

She advanced to second week at her home major for the first time.