The Ukrainian was forced to flee her home in Odessa last month amid the escalation of the Ukraine-Russia crisis and has embarked on an emotional run through this week's tournament.
Yet the 21-year-old wildcard admitted she has been overwhelmed by the support from across the globe amid her winning streak, crediting them for their help in her 7-6 (7-5) 4-6 6-4 victory on Saturday.
"It was a really tough match," Yastremska said. "In the third set, when I had match points and I lost that game, I was a bit crazy. I thought, I'm done, I've lost, because I don't have any more power.
"Then everybody was supporting me, and I felt like, 'you can do it'. I got a lot of messages from French people and from all over the world. But when I arrived here, I didn't expect I would get that huge support."
Yastremska will face Zhang Shuai in Sunday's final, after the Chinese eighth seed defeated French home favourite Caroline Garcia 6-2 7-5.
For Yastremska, it will be her first final since losing to Ash Barty in Adelaide at the start of 2020 – her only previous tournament success came in Strasbourg the year before.
The 21-year-old broke serve five times on her way to a 6-2 6-3 victory over Spain's Cristina Bucsa in an hour and five minutes, booking a quarter-final place.
Yastremska fled war-ravaged Ukraine last week, along with sister Ivanna, escaping through Romania but leaving their parents behind in Odessa after Russia's invasion began.
The three-time WTA tournament winner has spoken of the decision by her mother to stay with her father, and how that left the sisters tearful and agonising over when the family might be reunited.
Yastremska began her campaign in Lyon with a gruelling three-set win over Ana Bogdan and followed up impressively by sweeping aside Bucsa.
"Today, definitely it was a little bit easier. With my emotions, I could keep them under control, so I'm very happy with that," Yastremska said in an on-court interview, broadcast on Amazon Prime.
"I tried yesterday to recover myself as fast as possible to prepare for my match today. Still, I was very nervous because I wanted to win the match for my country.
"This tournament is very emotional for me, but I'm very happy with the win today. To be honest I'm very happy that I'm here, that I'm in a safe place with my sister."
The former world number 21, now down at 140 in the WTA rankings, was joined in the last eight by Zhang Shuai of China and France's Caroline Garcia.
Also going through to the quarter-finals on Thursday was Vitalia Diatchenko, a Russian playing under a neutral flag this week. She beat Swiss third seed Viktorija Golubic in three sets.
In a closely contested battle, Gauff was just a little too good, winning 52 per cent (91-of-176) of the total points, while creating 11 break point opportunities compared to nine for Zhang.
It continues a terrific run of form for the 18-year-old, who will break into the top 10 of the world rankings for the first time when it updates this coming week.
Speaking to the media after advancing to the quarter-finals, Gauff compared the atmosphere inside Arthur Ashe Stadium – where she has played every match this tournament – to an NBA game.
"It's way different [to a normal tennis crowd]," she said. "On the 6-5 changeover, people were saying 'let's go, Coco' – I was literally trying not to smile.
"I was, like, I've got to stay in the zone. Inside I was trying my hardest not to smile. This is a surreal moment for me – on Arthur Ashe Stadium and people are chanting my game. I feel like I'm at an NBA game.
"That's a special thing about tennis. When you go to a football game or an NBA game, people are chanting the team's name. That's great as a player.
"For you to have the whole crowd chanting your name specifically is something I won't take for granted."
When asked if the incredible attention she has received this week has been a distraction, she said it only helps her in the heat of the contest.
"I think it depends on the player – for me though, I just feed off of it," she said. "I think it helps me more.
"I mean, for some players, they prefer a more chill, relaxed environment. For me, if anyone has seen me play, I like to get pumped up. The New York crowd seems to like it too."
A meeting with the in-form Caroline Garcia is scheduled for the quarter-final, and she said it is no secret that she is one of the hottest players on tour right now.
"I think she's playing the best tennis she's played in a long time," she said. "It's going to be a challenge.
"When you play these players that are hot, I think it's more of a mental challenge. You just gotta accept she's going to hit some great shots, because I know she will.
"I think my mentality has been great. I played I feel like two similar opponents, Maddie Keys, who can hit some unbelievable shots from the wings. Same with Shuai today. She was hitting some great shots.
"I think I was doing a good job of accepting it, clapping my hands, moving on to the next point. I think I'm going to have to do that for the next match."
Gauff and Garcia have played twice before, with the American winning both matches against the Frenchwoman.
The Chinese tennis player was said to be considering retirement in 2015 after 14 unsuccessful attempts at grand slams, though was convinced to keep fighting by friend and fellow competitor Sam Stosur.
Simona Halep at the 2016 Australian Open was the first scalp Zhang claimed at a major before she went on to reach the quarter-finals.
The 33-year-old, who has two grand slams titles in doubles with Stosur, has not looked back from that win over Halep and has made it to the second week at all four majors in 2022.
"This year, I already have three third rounds," Zhang said after her third-round win at the US Open. "Oh my god, I won six matches! Before I couldn't win one match in many, many years. How happy!
"That's why when we meet some players who want to stop or feels sad after the match, I always tell them next match, see how you are better.
"When I started the tour, how bad [were my] results? No one was worse than me. [These girls are] much better than me, right? You guys are still young. Keep trying."
Gauff awaits Zhang in the round-of-16 as the latter searches for a maiden major success and fourth singles title.
The Ukrainian wildcard secured her place in the last four on Friday with a 6-4 7-6 (7-3) victory over the Italian amid the war with Russia in her home country.
The 21-year-old fled Odessa with her sister last week, separating from her parents in the process, and has spoken about her desire to honour those back in Ukraine with a title.
She will face second seed Sorana Cirstea after the Romanian made short work of Anna Bondar with a 6-3 6-3 victory.
Elsewhere, Caroline Garcia toppled another seed after fighting back to beat Alison van Uytvanck 4-6 6-3 7-5. The home favourite knocked out top seed Camila Giorgi in the first round and has a semi-final clash against Zhang Shuai to look forward to.
Zhang did not have to sweat to make her place after Vitalia Diatchenko was forced to retire at three games down in the first set through injury.
Ukrainian Yastremska fled her hometown of Odessa last month amid the ongoing conflict between Ukraine and Russia, and embarked on an emotional run throughout this tournament.
Yastremska credited the support she received from across the globe as a motivating factor for her success after reaching the final, where she could not get the better of eighth seed Zhang.
China's Zhang had not lost a set all week, though she did falter as world number 128 Yastremska claimed the first set before succumbing 3-6 6-3 6-4.
Yastremska, 21, was twice two games ahead in the deciding set, at 2-0 and 4-2 up, but Zhang reeled off four straight games to take the trophy.
Zhang was keen to credit her opponent after the match, saying: "Big congrats to Dayana and her team for working so hard.
"I know it's a tough time for you, but you are a fighter, you play unbelievable tennis. You are the best. For sure, you will win a lot of tournaments. Keep going."
Yastremska announced she would donate her prize money to a charity to provide aid back home, saying: "If Ukrainian people are watching me, you guys are so strong, you have an amazing spirit.
"I try to fight for Ukraine and I want to say thanks to every single person for standing by us and showing everyone we have a really strong spirit."
Zhang was never in danger against her unseeded opponent, easing to a 6-2 7-6 (7-4) win to set up a last-eight clash with Tereza Martincova.
Martincova brushed aside number eight seed Magda Linette 6-2 7-6 (7-3) in their round-of-16 meeting on Wednesday.
Elsewhere, Viktorija Golubic beat Heather Watson 7-5 6-2, while the match between number three seed Camila Giorgi and Harriet Dart was suspended at the start of the third set after the Briton had made it one set each.
Meanwhile, rain caused havoc at the Rosmalen Grass Court Championships, with top seed Aryna Sabalenka's match against Arianne Hartono the only one to partially take place.
The match was called off for the day after Sabalenka had claimed the first set 6-2.
