The top half of the 2022 US Open draw kicked off their campaigns on Day 2 of the tournament, and World No.1 Iga Swiatek was among the Top 10 players in action. Here's how they fared:
 Iga Swiatek (POL) d. Jasmine Paolini (ITA) 6-3, 6-0
Swiatek has played down expectations ahead of the fourth major of the year. Since her 37-match winning streak, the longest of this century, was ended by Alizé Cornet in the third round of Wimbledon, the Pole won just four out of seven matches before the US Open. In the run-up, she was open about her dislike of the balls used at Flushing Meadows.
But this emphatic 67-minute win was a reminder that, even out of her comfort zone, the 21-year-old can still be a destructive force. Swiatek smacked 14 winners to Paolini's five, and was ruthless in converting seven of nine break points.
The No.56-ranked Italian battled hard, breaking back twice in the first set and then winning the point of the match in the second with a backhand winner after going to to toe with Swiatek for 27 shots. But it wasn't enough to halt Swiatek's momentum as the World No.1 powered to her 18th bagel set of the year.
"I think just we did huge work before the tournament to work properly, but on the other hand also chill out and find a proper balance," Swiatek said, after her win.
Swiatek will next face 2017 champion Sloane Stephens, who overcame Greet Minnen 1-6, 6-3, 6-3. Swiatek and Stephens squared off for the first time this month in Cincinnati, where Swiatek won 6-4, 7-5.
 Garbiñe Muguruza (ESP) def. Clara Tauson (DEN) 6-3, 7-6(5)
Muguruza has won two Grand Slam titles, but the US Open has been the major where she has had the least success. The 2016 Roland Garros and 2017 Wimbledon champion was only 10-9 at Flushing Meadows coming into her first-round battle against up-and-coming teen Tauson.
But Muguruza was able to prevail over the 19-year-old Dane in a hair over two hours, which could help to turn around a below-par 2022 for the former World No.1. Even with Tuesday’s win, Muguruza is still just 10-14 for the season.
"I'm pleased with this match," Muguruza said afterward. "Obviously I'm not taking any win for granted, especially this year. It's been a year where I haven't had many wins. So very happy to get this first round here in US Open. I've had some early exits here, so it was very important for me to go through this first challenge."
Behind heavy shots, Muguruza swept to a set-and-a-break lead at 3-2 in the second set. But Tauson, who won two WTA singles titles during her breakthrough 2021 before her 2022 has been marred by back injuries, used big serves and deft passes to fight back, eventually holding three set points at 5-4 0-40.
However, Muguruza refused to yield, fending off each of those chances to hold on and keep the second set going. A similar scenario occurred in the tiebreak, where Muguruza found sturdy serves and drew errors from her younger opponent to come back from 1-4 down, grabbing the topsy-turvy set for the win.
An even younger foe awaits Muguruza in the second round: 17-year-old qualifier Linda Fruhvirtova, who beat Wang Xinyu 6-3, 6-4.
 Jessica Pegula (USA) d. [Q] Viktorija Golubic 6-2, 6-2
American No.1 Pegula's relentless consistency has been the key to establishing herself in the Top 10 this year. She has not lost her opener at any tournament since Indian Wells in March, and enters the US Open fresh off a semifinal run in Toronto and a quarterfinal in Cincinnati.
Pegula delivered another rock-solid performance against the finesse of former World No.35 Golubic. She conceded just four points behind her first serve, and lost her serve only once. Pegula was also effective at taking the net away from her opponent, winning eight out of 11 points in the forecourt.
"Always a little nerves, I feel like, going out there for your first match," Pegula said. "I thought I did a pretty good job of handling it, got through rather quickly, which I feel could have been a very, very tricky opponent, especially somebody who qualified and has a lot of confidence on the courts."
Next up for Pegula will be Aliaksandra Sasnovich, fresh off a run to the Cleveland final last week. Sasnovich defeated qualifier Elisabetta Cocciaretto 6-2, 6-4.
 Aryna Sabalenka d. [Q] Catherine Harrison (USA) 6-1, 6-3
Last year's semifinalist Sabalenka has endured a somewhat torrid 2022, with her trademark power hindered at times by large batches of double faults. The latter had a lesser presence as she raced past No.243-ranked Harrison, though -- Sabalenka committed only four en route to a 1-hour, 28-minute victory.
Sabalenka's control over her heavy hitting was also impressive as she posted 28 winners to 13 unforced errors. UCLA alumna Harrison is having a career-best year after qualifying for her first two Grand Slam main draws here and at Wimbledon, but despite scoring a break back in each set, was unable to halt Sabalenka's momentum.
Sabalenka now has a tough second-round match lined up against upset artist Kaia Kanepi, who just missed the seedings this fortnight. Kanepi has beaten Sabalenka both times they have met, including at this year's Australian Open.
 Paula Badosa (ESP) def. Lesia Tsurenko (UKR) 3-6, 7-6(4), 6-3
Badosa had tallied just a single win over her three prior appearances in the US Open main draw, and she was close to another first-round ouster at the hands of 2018 US Open quarterfinalist Tsurenko.
However, after dropping the opening set, Badosa gritted through a topsy-turvy second set en route to victory. The Spaniard was unable to serve out the second set at 5-4 and 6-5, but she used heavy groundstrokes to force long returns from Tsurenko in the tiebreak.
Tsurenko began to struggle in the toasty conditions as the third set wore on, and Badosa eventually became the sturdier player in rallies as she squeaked out the victory after two-and-a-half hours.