Serena Williams' quest for a 24th Grand Slam title continued Saturday but she had to rally against a rejuvenated Sloane Stephens at the US Open.Williams lost the first set before prevailing 2-6 6-2 6-2 to reach the fourth round, her serve -- and legendary desire to win -- playing a big factor at Arthur Ashe Stadium in New York.Fans are being kept away this year due to the coronavirus pandemic, with the tournament operating a bubble similar to other sports. But there watching Williams was her daughter, Olympia, and husband Alexis Ohanian.The 38-year-old Williams faces another stern test on Monday when she meets Greece's Maria Sakkari -- who beat her last week.The turnaround for Williams against Stephens came at 2-2 in the second, when she saved a break point before breaking for 4-2 against the 2017 champion.Through the first five games of the second set, Stephens -- who wore a Black Lives Matter mask entering the court -- had been getting much the better of the baseline exchanges.She hit 13 winners and only five unforced errors in ground stroke exchanges while Williams tallied 14 unforced errors and just seven winners.After the key two-game swing, though, Williams raised her game. She didn't face another break point and finished with 12 aces.When Williams broke for 3-1 in the third, Stephens' chances all but evaporated.Confidence boostThe victory is sure to be a confidence booster for Williams after suffering upset quarterfinal losses at two warmup events when she held commanding leads. That included against Sakkari at the Western & Southern Open, when Williams led by a set and 5-3.If she goes all the way in New York, Williams would tie Margaret Court for the all-time lead in Grand Slam titles.Even in defeat, it's the type of outing that could kick-start Stephens' career. No one has ever questioned her talent but Stephens has struggled since reaching the French Open final in 2018.She entered the US Open with a 1-7 record in 2020 and only got a seeding of 26th when other players pulled out of the draw.Besides Williams' family, fellow players Naomi Osaka, Dominic Thiem, Sofia Kenin and Petra Kvitova took in the action from their luxury suites on Arthur Ashe that would otherwise go to corporate sponsors and guests.Saturday's most dramatic contest saw Karolina Muchova -- who beat Venus Williams in the first round -- save three match points to defeat Sorana Cirstea of Romania 6-2 2-6 7-6 (7).The Czech became the latest player to save match points en route to victory this week, following Andy Murray, Aliaksandra Sasnovich, Cameron Norrie and Varvara Gracheva.In a sizable upset in the men's draw, Canada's unseeded Vasek Pospisil beat Spain's Roberto Bautista Agut 7-5 2-6 4-6 6-3 6-2. The eighth-seeded Spaniard came close to ending Novak Djokovic's unblemished 2020 record last week at the Western & Southern Open in New York.text by Ravi Ubha, for CNNSee omnystudio.com/listener for privacy information.