NEW YORK, NY, USA -- No.4 seed Elina Svitolina has advanced to the fourth round of the US Open for the first time in her career on Saturday, stopping Shelby Rogers of the United States, 6-4, 7-5.

"It was very good level of tennis in the end of second set and the crowd was behind her," Svitolina told the press afterwards. "It was tricky, but I was very happy I could handle it, because it was, like, four or five very tough games. I was happy that it's all finished. Yeah, was happy with the performance."

Svitolina and Rogers had played twice before, and both previous encounters were long three-setters, including a two-hour and 22-minute tilt at the Brisbane International in January of this year. "Finishing in two sets, it's very good for me," Svitolina continued, "because last two matches we played, it was three sets."

This match was not as protracted, as it barely cracked 90 minutes, but it did not lack for drama. Svitolina took the first lead of the match for 3-1, but Rogers' powerful forehand, which served her well in this match, provided a winner on break point to put the first set immediately back on serve. Later, however, two poorly timed unforced errors off of that wing gave Svitolina the first set, 6-4.

Rogers broke first in the second set, racing out to a 2-0 lead, but then Svitolina reeled off five straight games with consistently strong play, and it appeared that the fourth seed would cruise to a smooth victory.

But a marathon game ensued at 5-4, as Svitolina initially served for the match. Three match points went unused, as Rogers' one-two forehand punches became more daring and effective. On the second break point of the game, Svitolina hit a backhand into the net, and the set was tied at 5-5.

But at 6-5, Svitolina regrouped, and executed solid groundstrokes which Rogers couldn't handle. Svitolina's bigger hitting at this juncture paid off, as a sharply struck forehand clipped the net cord and dribbled over for a winner on the Ukrainian's fourth match point.

"I think I was serving pretty good," Svitolina said after the match. "I was reacting, because she was, you know, striking the ball pretty good like she always does. I was expecting this, and I was trying to really react quick and be ready for her shots. I handled it well."

Rogers executed a solid strategy, moving forward frequently to finish points off at the net. She had a good success rate doing so, winning 20 out of 33 forays to that area. But Svitolina was too solid in the pivotal moments, keeping her unforced errors low and winning five of her seven opportunities to break.

Therefore, Svitolina's hopes of claiming the World No.1 ranking after the US Open are still alive. She will face a highly-ranked opponent in the fourth round no matter what, as she will contest her next match against either 15th-seeded American Madison Keys or No.17 seed Elena Vesnina of Russia.

"I know the way they play," Svitolina said, when asked about her upcoming fourth-round match. "I will just try to chill. You know, I'm in second week of a Grand Slam, so I'm really, really proud of the performance I showed."

Marathon matches: Two other matches, both first-time meetings, were extended tussles on a cloudy late Saturday afternoon in Flushing Meadows.

Kaia Kanepi, a five-time Grand Slam quarterfinalist and former World No.15, got past Japanese teenager Naomi Osaka, 6-3, 2-6, 7-5, in two hours and three minutes. The 32-year-old Estonian is coming back from injuries, and, ranked World No.418, had to navigate the qualifying this year at the US Open.

"Right now, I feel great; it was really amazing to win the match," Kanepi told the media after her match. "I wasn't sure last year, in December, if I was ever coming back at all."

In a match between two of the hardest-hitting players in the draw, it was the veteran's experience that won out in the end. Kanepi came back from 0-30 down on her serve at 5-5 in the deciding set to hold, and then broke for the match at 6-5 by forcing an error from Osaka's backhand on match point.

The 19-year-old Osaka has made the third round at five of the seven majors she's contested, which is why she is ranked No.45 in the world. But she has not yet broken that barrier, and hitting 49 unforced errors (as opposed to 26 winners) was not good enough against Kanepi.

"I think I stressed myself a little bit after playing Kerber, and I just had more expectations with myself," an upset Osaka theorized in her press conference. "So I think the next Grand Slams, if I happen to beat a really good player, I'm just going to take that one match at a time and just play within myself."

Meanwhile, Kanepi, a 2010 US Open quarterfinalist, was aggressive and often moved forward, and it paid off for her, winning 16 of 18 points at net.  She advances to play crafty Russian Daria Kasatkina, ranked World No.38, in the fourth round.  

American Jennifer Brady won an even longer match, triumphing over Romania's Monica Niculescu, 6-3, 4-6, 7-6(3), in two hours and 26 minutes.

This was a contrast in styles from the very beginning, as the formidable power game of the 22-year-old American was matched up against the unorthodox shotmaking of the 29-year-old Romanian.  It was Brady who raced through the first set, hitting 4 aces and out-winnering Niculescu 12 to 2.

But the clever Romanian rebounded in the second set, breaking Brady 4 times and hitting 15 winners to only 13 unforced errors.

The match went all the way to a final-set tiebreak, and when Brady raced to a 4-0 lead, the match appeared all but over. Niculescu, however, made the tiebreak more competitive, hitting a funky volley at 4-3 that had Brady scrambling and ultimately falling on court while laughing at her effort.

"It didn't, like, occur to me that, you know, I was on the ground. I was just, like, oh, I don't want to get up and play right now," Brady joked in her post-match press conference. "I was tired, and, you know, laying there felt nice. It was a tough match mentally and physically."

Niculescu closed the gap to 5-3, but Brady won the final two points of the tiebreak, clinching the victory with a powerful crosscourt backhand that Niculescu could not return on match point.

Brady has now made the fourth round of a major for the second time in her career -- she has completed this task at both hardcourt Grand Slams this year, as she reached the round of 16 at the 2017 Australian Open, as a qualifier.

Her reward this time: a date with World No.1 Karolina Pliskova, who Brady will try to upset in order to claim a spot in her first major quarterfinal.

"She's a big hitter, she has a very good serve," said Brady about Pliskova. "It's always an honor to play, you know, the players at the top of the game. I'm just going to go out there and have some fun."