With a sure-to-be-hyped rematch with Serena Williams in the offing at the US Open, Sloane Stephens held up her end of the bargain.
Stephens then needed to wait several hours after her victory to find out whether Williams would join her in the next round. Turns out she will — Williams coasted past Yaroslava Shvedova, 6-3, 6-1, in a match that wrapped up past 1 a.m. Saturday.
From the moment the women’s draw came out at Flushing Meadows, it was clear which potential fourth-round match was the most intriguing: defending champion Williams against up-and-coming talent Stephens.
‘‘It’s something I think everyone is looking forward to,’’ Stephens said.
Stephens reached the round of 16 in New York for the first time by beating 23d-seeded Jamie Hampton, 6-1, 6-3, Friday.
‘‘Serena is the No. 1 player in the world. She’s possibly the greatest player of all time. Sloane is Sloane. You know, she’s making her own name. She’s top 20 in the world for a reason,’’ Hampton said. ‘‘They’re both great players, both great competitors.’’
Hampton’s blase summation of a Williams-Stephens matchup: ‘‘I don’t really make too much of it.’’
She might be the only one.
Williams and Stephens have played twice in the past — both in January, both on hard courts, both in the quarterfinals. Williams won, 6-4, 6-3, at the Brisbane International. Three weeks later, Stephens came back for a 3-6, 7-5, 6-4 victory in Melbourne.
Stephens has reached at least the fourth round at all four Grand Slam tournaments this season, including a semifinal run at the Australian Open and a quarterfinal berth at Wimbledon, losing to the eventual champion in both.
‘‘She just likes the big matches, you know,’’ the 23-year-old Hampton said. ‘‘She shows up to play at the Slams, for sure.’’
Stephens-Hampton was the first match in Arthur Ashe Stadium between two American women younger than 24 since the Williams sisters met in the 2002 final.
And Stephens dominated, in part because she handled the occasion far better than Hampton did. Stephens limited herself to 15 unforced errors; Hampton made 34.
Afterward, Hampton blamed her own jitters, saying she’s been working with a sports psychologist to improve her mind-set when the stakes are most significant.
‘‘I've had tendencies, shown tendencies, to play really bad in big moments,’’ Hampton said. ‘‘I'm incredibly, incredibly disappointed in the way I played today.’’
Stephens might say the same about how she shows up at lower-tier tournaments. While her Grand Slam record this season is 15-3, she is only 17-15 at other tournaments, with six losses in the first or second round.
‘‘The Grand Slams — it’s just showtime, I guess,’’ Stephens said, shrugging her shoulders. ‘‘What can you do?’’
Nothing to see here
It was a ho-hum afternoon without any significant surprises.
During the day session, the only seeded man to bow out was No. 17 Kevin Anderson, a 6-2, 6-2, 6-2 loser against 2006 Australian Open finalist Marcos Baghdatis, while all seven women’s matches were decided in two sets. Winners included 2011 French Open champion Li Na, 2012 Wimbledon runner-up Agnieszka Radwanska, and 2008 US Open runner-up Jelena Jankovic.
Defending champion Andy Murray and top-seeded Novak Djokovic experienced brief lulls before staying on course for a possible showdown in the semifinals.
Martina Hingis closed out the first match in her return to Grand Slam tennis with back-to-back double faults in a6-3, 7-5 doubles loss to top-seeded Sara Errani and Roberta Vinci at the US Open. Later, Hingis and Mahesh Bhupathi fell, 7-6 (7-5), 7-6 (7-5) to Chan Yung-jan and Robert Lindstedt in a mixed-doubles match marked by a number of disputed calls in the second-set tiebreaker.
Hingis, the 32-year-old who was inducted into the International Tennis Hall of Fame last month, was partnered with Daniela Hantuchova for her first appearance at a major since retiring in 2007.
Trailing, 6-5, in the second set, Hingis served three double faults, including the last two of the match. Moments later, she sat down and buried her face in her towel.
Bryans on track
American twins Bob and Mike Bryan stayed on track to become the first men’s doubles team to complete a calendar-year Grand Slam since 1951, beating Eric Butorac and Frederik Nielsen, 6-3, 6-2, in the second round in Flushing Meadows.