From the moment the women's draw came out at Flushing Meadows, it was clear which potential fourth-rounder was the most intriguing: defending champion Williams against up-and-coming talent Stephens, the top two Americans in the rankings.
"As I always say, I think it will be epic," Stephens said. "I'm really looking forward to it. See what happens."
And that statement came hours before Williams advanced out of the third round by beating 78th-ranked Yaroslava Shvedova of Kazakhstan 6-3, 6-1 in a match that wrapped up at 1:05 a.m. ET Saturday.
"I'm so excited you guys stayed out for the late-night rendezvous. Thank you, guys, for staying," Williams told the Arthur Ashe Stadium crowd. "I don't think I've ever played this late."
Williams has dropped a total of eight games through six sets this week. After killing time before facing Shvedova by watching "I Love Lucy" on a computer tablet, Williams produced a 22-3 edge in winners. She faced only one break point, erasing it with one of her six aces, then following up with another at 119 mph.
As for facing Stephens on Sunday, Williams said: "I definitely look forward to it. Whatever happens ... an American for sure will be in the quarterfinals, which is really good."
Stephens reached the round of 16 by beating 23rd-seeded Jamie Hampton 6-1, 6-3 in an another all-American tilt earlier Friday.
The 15th-seeded Stephens beat Hampton in the first match at Arthur Ashe Stadium between American women younger than 24 since the Williams sisters met in the 2002 final.
Stephens has reached at least the fourth round at all four Grand Slam tournaments this season, including a semifinal run at the Australian Open in January, when she upset Williams in the quarterfinals. That's one of only four losses in 67 matches for the top-ranked Williams in 2013 (Victoria Azarenka beat her twice, and Sabine Lisicki once).
Stephens lost in the third round at Flushing Meadows each of the past two years, beaten by 2008 French Open champion Ana Ivanovic both times.
After Friday's match, Hampton blamed her own jitters, saying she's been working with a sports psychologist to try to improve her mindset 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?"
The fifth-seeded Li avenged her third-round upset loss to the young Brit at last year's US Open, winning in straight sets at the same stage at Flushing Meadows.
Li, the 2011 French Open champ, rallied from down a break in the second set for a 6-2, 7-5 victory.
Li was nervous after she noticed that her draw was a repeat from last year. A pep talk from coach Carlos Rodriguez eased her anxiety.
"After the talk I was feeling much, much better," she said. "Because before I never try to share the feeling with the team."
In other action, Agnieszka Radwanska needed nearly two hours to slip past No. 32-seeded Anastasia Pavlyuchenkova 6-4, 7-6 (1). The third-seeded Pole faced 10 break points, but Pavlyuchenkova was able to convert only two, while Radwanska was 3-for-5.
Wimbledon runner-up Lisicki, seeded 16th, won't be making a run after she was eliminated in straight sets by Ekaterina Makarova. The 24th-seeded Russian won 6-4, 7-5.
A year ago, Robson's upset of Li was the biggest victory of her breakthrough run. Meanwhile, it was the third straight frustrating US Open loss for the Chinese star.
Robson was ranked 89th going into last year's tournament. She had never advanced past the second round at a Grand Slam event or defeated a top-10 opponent.
That all changed when she upset major champions Kim Clijsters and Li back to back to make the fourth round. Now 19, Robson was seeded 30th at Flushing Meadows and coming off a fourth-round run at Wimbledon.
Li had 34 unforced errors in their match a year ago, and she lamented then that the free points lifted the teen's confidence. This time, Robson never had much of an opening.
"She served very well today, and I thought she was returning really deep," Robson said. "You know, there wasn't a lot I could do in some points."
Li surprised herself with 11 aces Friday -- including one on a second serve on match point -- and won all nine points when she went to the net. She's in the fourth round at the US Open for the first time since 2009.
Her run over, Robson now must face an unfortunate reality for many teenagers: getting her wisdom teeth out.
"All the other girls in the locker room are telling me their horror stories: 'Oh, yeah, I pulled my gauze out and it was just blood,'" Robson said. "So that's not too nice."
Hingis, who was inducted into the International Tennis Hall of Fame last month, was partnered with Daniela Hantuchova on Friday 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.
The 32-year-old Hingis won five major singles titles and nine more in women's doubles from 1996 to 2002.
Information from The Associated Press was used in this report.