NEW YORK, NY, USA - The New York City Public Schools don't resume classes for another two weeks, and though Kiev-born Marta Kostyuk won't feature on any attendance rosters, the fast-talking teen played like summer vacation will never end at the 2018 US Open, surviving Moscow River Cup quarterfinalist Valentyna Ivakhnenko, 4-6, 7-6(6), 7-6(4).

"I thought I was gonna lose the match from the first point," a frank and exhausted Kostyuk admitted after saving six match points on Tuesday. "I didn’t feel really good today, but that’s how you play; I mean, you have to win, even in bad days.

"I’m really, really happy with the win, because I hadn't won any good matches for a long time, since Wimbledon. Granted, I played only one match in that period, but I'm still really, really happy."

Kostyuk first made waves on the junior circuit last season, winning the Australian Open as a 14 year old; a year later, she was in the main draw of the women's event, barreling into the third round where she played countrywoman Elina Svitolina.

Since then, she enjoyed a solid run at the Porsche Tennis Grand Prix in Stuttgart - pushing Caroline Garcia to three sets as a qualifier - but is looking for another big result in the last Grand Slam tournament of the year.

"It was really tough, because it was sunny, it was a lot of heat today. For the past four days in New York, it was rainy and no sun, so it wasn’t that hot, so I didn’t get used to this temperature. I don’t know, it was really tough. I was dying the whole match."

New coach Dmitriy Brichek helped to keep her alive on Court 9 as she battled frustration and an in-form opponent to rally from a set and a break down, saving two match points in the second set and four more in the third as the Ukrainian 16-year-old served for force a final set tie-break.

Also in her corner was Brichek's former charge, World No.35 Lesia Tsurenko. Standing in the shade for most of the match, Tsurenko was living and dying with each point, giving an enthusiastic synopsis of Kostyuk's comeback after the second set.

"I saw that Marta was playing really aggressive and was trying to make a lot of winners, but it didn’t work all the time," she noted. "But I saw at the end of the set that the percentage of the successful points was getting higher and higher. I think that’s the key how she won the set. Some points, she was just super aggressive. This is something unbelievable, and I think this is what makes her unique."

Tsurenko made it to the second week of the US Open back in 2016, making it through a similarly oppressive afternoon to defeat Dominika Cibulkova en route to the fourth round. Telling selfie-seeking fans she was only here to watch her friend fight back, the two-time Abierto Mexicano Telcel champion felt there was always something special about Kostyuk.

"She was always good, and everyone was saying that she can be the future of the Ukrainian tennis and she can be really good. At that age, you never know, because we have so many good kids.

"Now I see that she can really play well, and I really support her. Sometimes we practice together, and I like her personality, she’s really smart. She’s 16 but she’s already really smart. My ex-coach is working with her now, so for me, her success is, like, I’m really happy for her success."

Kostyuk is one of several talented Ukrainian youngsters, including 18-year-old Dayana Yastremska - who will make her Grand Slam main draw debut next week - Anhelina Kalinina, and Katarina Zavatska, both in action this week in qualifying.

"In Ukraine, we always have many good juniors, and now the question for my country is the transition from juniors tennis to professional," Tsurenko says. "We could always have more and more players - I would be happy if we will get like as more as possible! - but I think this is the key now, that our good juniors, they should become good professional players."

Signing autographs and taking pictures after the match, Kostyuk looked quite convincing as a professional in the making, booking a second round encounter with 2014 US Open junior champion Marie Bouzkova, and will take all the support she can get on the journey there.

"I appreciate Lesia being here; it really means a lot. We try to support each other, so like this week, we'll watch each other's matches. The atmosphere was so great here, I want to thank everyone who came to watch me play, because it was really nice."