NEW YORK, NY, USA -- Sloane Stephens' superlative summer sees her into the final sixteen at the 2017 US Open.

In the first meeting between two players who have recently experienced rapid ranking rises, the American eliminated Ashleigh Barty of Australia on Friday, 6-2, 6-4, and she advances to the fourth round in Flushing Meadows for the first time since 2013.

"I thought I played all around pretty solid," said Stephens, in her post-match press conference. "I mean, obviously Ash is a great player. She's tricky to play because she does a lot of different things. I was happy that through everything that she kind of gave to me, I was able to just stay consistent and play my game."

After a lengthy injury layoff, Stephens has been on a blistering run coming into the US Open, registering semifinal results at the Rogers Cup in Toronto and the Western & Southern Open in Cincinnati, which pushed her ranking up over 800 spots to her current ranking of No.83.

Barty has also posted an incredible rise in 2017, winning her first career title at the Alya Malaysian Open in Kuala Lumpur, and reaching the final of the Aegon Classic Birmingham. After starting the year at No.271, she is up to World No.43.

The match started inauspiciously, as Stephens hit five unforced errors to get broken in her first service game, followed by Barty handing the break back, in part due to two double faults. Stephens found her sea legs first, breaking for 3-1 and staving off four break points in the following game to hold for 4-1.

Barty is very comfortable moving forward, but started rushing the net at inopportune moments, and Stephens hit two consecutive exceptional passing shots to reach double set point at 5-2. One more unforced error off the Barty backhand gave Stephens the first set.

Stephens’ speed and depth of shot were sublime in the opener, but Barty had opportunities to make the set much closer. However, the 21-year-old Australian could only convert one of her eight break points in the set. Moreover, she was only 3-of-10 at the net during that timeframe.

And, in fact, the second set was much closer.  Stephens found herself behind in every one of her service games, and it was Barty who claimed the first break for 2-1, courtesy of a backhand winner.

But Stephens broke back immediately off a forehand error by Barty while down break point. Overall, despite the circuitous Stephens service games in the second set, Barty could only break twice.

It was Stephens who broke three times in the second set; of course, most crucially at 5-4, when one final forehand winner gave her the 76-minute victory. The American hit 18 winners to the Australian's 16, and Barty will rue her 31 unforced errors and 3-for-11 break point conversion rate in the match.

Stephens will hope to keep that winner count up when she goes looking for her first US Open quarterfinal -- and first Grand Slam quarterfinal since 2013. "I haven't been in the second week of a slam in a long time," Stephens said after the match. "It's nice. Excited to be here. Especially at a home slam. I mean, nothing really better."

No.30 seed Julia Goerges will be Stephens' next opponent. The 28-year-old German rolled into the fourth round on Friday, with a 6-3, 6-3 win over Aleksandra Krunic of Serbia. It is Goerges' first appearance in the round of 16 in Flushing Meadows.

Goerges had an excellent serving day, surviving all three break points that Krunic had in the match, and she also broke her opponent three times. The hard-hitting German had an astounding 27 winners in the 72-minute match, almost doubling her unforced error count.

World No.78 Krunic, who upset No.7 seed Johanna Konta in the first round, put up a strong fight, but Goerges is still in the form that has seen her reach three WTA finals this year and the quarterfinals of the Western & Southern Open earlier this month.

It was Stephens who ended that run by Goerges in Cincinnati, but if Goerges maintains a nearly 2-to-1 ratio between her winners and unforced errors, as she did today, she will be a challenging opponent for Stephens -- or anyone else left in the draw.

Suárez Navarro, Sevastova survive: World No.35 Carla Suárez Navarro of Spain got past a determined opponent in World No.40 Ekaterina Makarova of Russia, winning 6-1, 3-6, 6-3 in one hour and 41 minutes.

The Spaniard was pristine in the first set, winning both of her break points, but Makarova had 13 unforced errors to only 2 winners in the opener.

The final two sets were much tighter, but Suárez Navarro was able to hold on from a 5-1 lead in the decider to make the US Open fourth round for the fourth time.

"I start really good, but then the match was so close, and then I was fighting all the time," Suárez Navarro told the press after the match. "I was nervous, and it's not easy. But I'm happy with the way I finished the match."

Suárez Navarro will now play No.9 seed Venus Williams in an attempt to make a second US Open quarterfinal in her career after this injury-plagued season.

"Now I'm feeling really good," Suárez Navarro continued after the match. "I'm playing with no pain, so I'm happy with play like this."

Later in the evening, No.16 seed Anastasija Sevastova of Latvia booked a spot in the fourth round, with a comprehensive win over Croatia's Donna Vekic, 6-2, 6-3.

"I think I started pretty well," Sevastova told the press after the match. "It was competitive in the beginning, but I just hung in there and moved well."

Sevastova led 5-1 in each set, but both times the Latvian failed to serve out the set in her first attempts. It became extremely tense when she went down double break point during her second attempt to close out the match, but she pulled the game back to deuce, and two wayward backhands by Vekic gave Sevastova her desired result.

"I just got the better of it -- it worked pretty well mixing it up," Sevastova continued. "It actually should have been 6-1 in the second set, because I was totally in control -- but I’m not a robot!" she laughed.

"I got a little bit tight," the 16th seed concluded, "but I'm happy that I won."

Sevastova made her first Grand Slam quarterfinal at the US Open last year; to repeat that performance, she will have to beat the winner of the late match between two wild cards: Sofia Kenin of the United States, and 2006 US Open champion Maria Sharapova of Russia.