The world number one was forced to come through a testing last-four encounter with American Danielle Collins but got a victory that ensures she will remain top of the rankings after the first major of 2020.
Her power posed Barty plenty of problems and another shock appeared on the cards when Collins, who defeated Sofia Kenin and Belinda Bencic en route to the semis, claimed the first set.
Collins struggled on serve in the second set, however, and Barty was ruthless in capitalising as she raced into a 5-0 lead.
Powerless to prevent Barty forcing a decider, Collins demonstrated admirable resilience in the third set.
Barty broke for a 4-3 lead with a return winner, but Collins' vicious backhand saw her hit straight back.
The same shot proved her downfall in the decisive tie-break, though, a backhand error securing the match for Barty, who will turn her attention to one of the WTA Tour's rising stars in Yastremska.
Ranked 24th in the world, the 19-year-old overcame world number 12 Aryna Sabalenka, adding the Belarusian to a list of scalps that has this week also included Angelique Kerber.
Sabalenka saw off Simona Halep in the quarter-finals but Yastremska had too much for her as the Ukrainian completed a 6-4 7-6 (7-4) success.
"Especially in the beginning of the year, I think it brings me some confidence before the grand slam, so it's nice to be in the finals," Yastremska said after reaching her first WTA Premier final.
"Here I started really to feel, with each game, that I'm playing better and better."
Meanwhile, at the Hobart International, Zhang Shuai overcame Veronika Kudermetova to set up a final with Elena Rybakina, who beat 2015 champion Heather Watson.
Home hope Barty benefited from a bye into the second round, but no one could accuse her opponent of allowing her an easy stroll into the last eight, the world number one eventually coming out on top 4-6 6-3 7-5 after two hours and nine minutes on court.
The French Open champion was beaten by Jennifer Brady in her opening singles contest of 2020 at the Brisbane International last week and was in danger of falling at the first hurdle again on Tuesday.
Barty raised her game after losing the first set before a thrilling decider swung back and forth with a total of five breaks of serve, including when the top seed was twice serving for the match at 5-2 and 5-4.
But the Australian bounced straight back with a break of her own to move 6-5 in front and then served it out at the third attempt to set up a meeting with either eighth seed Marketa Vondrousova or Arina Rodionova, the Australian qualifier who surprisingly saw off Sloane Stephens 6-2 6-2 in the first round.
Joining Barty in the quarters is Wimbledon champion Halep, who dealt with another Australian in the form of wildcard Ajla Tomljanovic 6-4 7-5 in her first singles contest of the season.
The second seed from Romania, who struck 19 winners and made only 11 unforced errors, will now face Aryna Sabalenka or Bernarda Pera in the final eight after they defeated Su-wei Hsieh and Barbora Strycova, respectively.
Maria Sakkari, Donna Vekic and Julia Goerges came through first-round ties.
Top seed Elise Mertens eased into round two of the Hobart International, thrashing Christina McHale 6-1 6-1, and Garbine Muguruza advanced with a 6-1 7-5 defeat of Wang Yafan.
Caroline Garcia, the eighth seed, was send packing by Australian outsider Lizette Cabrera on a day which also saw Elena Rybakina, CiCi Bellis, Alize Cornet, Ons Jabeur and Zhang Shuai go through.
Bencic was due to go up against Veronika Kudermetova in the second scheduled semi-final on Friday, only for the Russian to withdraw due to a hip injury.
It was a similar story for Kasatkina, who received a walkover after Paula Badosa pulled out of their match, citing a thigh problem.
While Bencic and Kasatkina will now get the chance to claim a trophy early in the season, the focus for Badosa and Kudermetova will be on regaining fitness in time for the Australian Open, which starts next week.
Badosa was confident she can recover for the upcoming major, where she has been drawn against American Caty McNally in the first round.
"I'm really disappointed that I had to withdraw because I was really looking forward to the match," Badosa told reporters.
"When I was playing [against Beatriz Haddad Maia], it was a very tough match, especially physical, so I felt a little bit in my abductor. I felt like I pulled it a little bit.
"I feel a little bit worse, so I have the Australian Open ahead, and I hope I can recover for that."
Badosa needed two hours and 35 minutes to get past the Brazilian on Thursday, having knocked off Anett Kontaveit and Kaia Kanepi in the earlier rounds.
"I played three really good matches," the Spaniard said. "I think that helps me, as well, on my confidence for the tournaments ahead. Now it's something that I cannot control, so it is what it is."
At the Hobart International, Elisabetta Cocciaretto set up a showdown with Lauren Davis.
Sofia Kenin, the 2019 champion, fell 7-5 4-6 6-1 to world number 67 Cocciaretto, who has reached her first Tour-level singles final.
"It’s unbelievable for me to be here in the final of such a great tournament, and I’m really happy about my performance," Cocciaretto said.
"[Kenin is] a very good player, I was a junior when she won the grand slam [2020 Australian Open], so for me it's an honour to play against her."
Davis, meanwhile, saw off Anna Blinkova in straight sets. She has not featured in a Tour-level final since clinching the trophy in Auckland in 2016.
Both Bencic and Kasatkina did not have to play a semi-final after their respective opponents, Veronika Kudermetova and Paula Badosa, both pulled out with injuries.
Bencic romped to victory in the final though, dropping just two games against her Russian opponent to lift her first title in Australia.
The match lasted just 67 minutes, as the 2021 runner-up converted five of her seven break point opportunities while not facing a single break point herself.
Bencic rattled off eight games in a row to start the final, and though Kasatkina did save some face with a couple of holds late on, the world number 13 finished the job to win in straight sets ahead of the start of the Australian Open next week.
"I'm happy I could show my work here on the court," Bencic told reporters at a post-match news conference. "I thought I played some great matches from the start of the tournament and also against different kind of opponents so I really could test myself out there in every way and just go confidently into the Australian Open."
At the Hobart International, Lauren Davis ended a six-year title drought with a 7-6 (7-0) 6-2 triumph over Elisabetta Cocciaretto in an all-unseeded final.
In the opening set, every game went to serve until the tie-break, when Davis found three crucial breaks to take the advantage heading into the second stanza.
But the second set was not the same tight affair as Cocciaretto, playing in her first Tour-level singles final, collapsed to a 5-0 deficit to leave her staring down the barrel of defeat.
Davis, who herself was playing in a first Tour-level final since winning the trophy in Auckland in 2017, overcame losing the next two games to take the title having not lost a set at the tournament.
Davis was delighted after the match, saying: "I have a lot of emotions going through my body right now. I'm just really happy, really excited. I really had to play my best in order to win today."
The Kazakh, 20, proved too good for Zhang Shuai 7-6 (9-7) 6-3 to claim her second WTA Tour crown.
Rybakina is in impressive form to begin the year, having also reached the final in Shenzhen this month.
She delivered in the decider this time, converting all three break points she created on her way to victory in one hour, 33 minutes.
Rybakina will hope to carry her good form into the Australian Open, facing Bernarda Pera in the opening round.
Kerber, who won the Australian Open in 2016, had lost the first set to Dayana Yastremska 6-3 and was a break down in the second when she required on-court medical assistance.
After being put through a series of stretches, the former world number one decided she was unable to carry on and retired, allowing Yastremska to reach the last eight of the competition, where she will meet Donna Vekic after her 2-6 7-5 6-1 win over Maria Sakkari.
The most impressive win of the day belonged to Marketa Vondrousova, however, as last year's French Open runner-up claimed a stunning 6-0 6-0 victory over home hope Arina Rodionova, setting up a meeting with another Aussie in the quarters – world number one Ash Barty.
Vondrousova, 20, is taking part in her first tournament since Wimbledon after undergoing wrist surgery in September and will be out for revenge against Barty, who beat her at Roland Garros in June.
Fourth seed Belinda Bencic came through a tight tussle with Julia Goerges to emerge a 7-6 (8-6) 7-6 (7-4) victor, with her last-eight opponent Danielle Collins having significantly less difficulty against fellow American Sofia Kenin – the unseeded 26-year-old winning 6-3 6-1.
The fourth quarter-final will see Aryna Sabalenka go head-to-head with Simona Halep, after the Belarussian sixth seed eliminated Bernarda Pera 7-6 (7-4) 6-2.
Elise Mertens remains on course for a third Hobart International title after the top seed dropped single game in her 6-1 6-0 defeat of Viktoria Kuzmova, setting up a quarter-final with Great Britain's Heather Watson, a 7-6 (7-5) 6-3 winner against Fiona Ferro.
Aussie wildcard Lizette Cabrera claimed a 4-6 6-4 6-4 upset over Kristyna Pliskova, while second seed Garbine Muguruza edged past Ons Jabeur 3-6 6-3 7-6 (7-4) and will face Veronika Kudermetova.
Shuai Zhang, Lauren Davis and Elena Rybakina are also into the quarter-finals following respective triumphs over Kateryna Kozlova, Magda Linette and Alize Cornet on Wednesday.
Former world number one Muguruza withdrew from her quarter-final against Veronika Kudermetova on Thursday.
The two-time grand slam winner is scheduled to face a qualifier in the first round of the Australian Open on Tuesday. She is in the same quarter of the draw as Karolina Pliskova, Elina Svitolina and Angelique Kerber.
Muguruza tweeted: "I'm sorry I could not play today. I've had a fever for several days and this morning my body said 'enough'.
"I'll rest today and hope to travel to Melbourne tomorrow. I hope to be able to play [the Australian Open].
"I want to thank all the fans in Hobart for their support and love. I hope to return soon."
Heather Watson beat top seed Elise Mertens 6-7 (5-7) 6-4 7-5 to reach the semi-finals, while Kudermetova will take on Zhang Shuai.
At the Adelaide international Simona Halep suffered a 6-3 6-2 quarter-final loss to Aryna Sabalenka.
Second seed Halep lasted just one hour and nine minutes against Sabalenka, who reeled off seven straight games to take the first set and move 5-0 up in the second.
The Wimbledon champion won the next two games but was unable to hold serve to stay in the match.
Sabalenka will take on Dayana Yastremska, who beat Donna Vekic 6-4 6-3, in the semi-finals.
Top seed Ash Barty repeated her French Open final victory over Marketa Vondrousova to reach the final four in Adelaide.
Barty hit 20 winners and saved six of seven break points to secure a 6-3 6-3 triumph and advance to a meeting with Danielle Collins after the American overcame Belinda Bencic 6-3 6-1.
