Her come-from-behind win ended top seed Barty's hopes of becoming the first home victor at the Australian Open in 43 years after Chris O'Neil's breakthrough in 1978. Ash started very good.
Barty wasted no time in stamping her authority on the contest and looked to be coasting when she conceded only six points in racing to a 5-0 lead in just over a quarter of an hour, wrapping up the first set soon afterwards.
"When you call for the trainer, you tell the umpire what the reason is", she said. "You're either winning or you're learning, and today is a massive learning curve for me".
However, Muchová took a nine minute medical timeout after the first set - before staging a comeback to gain full control to win the second set 6-4 and clinched the decider 6-2.
Muchova awaits the victor of the all-American quarterfinal between Jennifer Brady and Jessica Pegula, with all three women looking to play in their first grand slam final, with only one prior semifinal appearance between the trio. "I just asked for help".
Barty had no complaints about Muchova halting play. When the Czech returned, she played much better.
"It's within the rules", Barty said.
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"Without a doubt it's disappointing, but we learn and move on and don't let it ruin what has been a really successful and enjoyable start to the new season".
Barty continued to carve out chances on Muchova's serve but failed to convert them and her error count soared as she tried to finish points too early to wrest back the momentum.
Muchova had some treatment at her chair early in the second set and then took a lengthy medical timeout, returning to court revitalised and ready to take the match to the former French Open champion.
With Barty the only grand slam champion left in her half of the draw, the 24-year-old had been a hot favourite to at least become the first home hope to make the women's Open final since Wendy Turnbull in 1980.
"I started to feel a bit lost by the end of the first set and my head was spinning, so I took a break", Muchova explained after the match. Muchova came out of the break and broke Barty the next game, who lost all four points on her racket with unforced errors.
That 10-minute pause in the match proved to be the catalyst for a stunning turnaround, and one which will likely haunt Barty for some time.
Muchova's only other victory over a Top 5 player was against No. 3 Karolina Pliskova at Wimbledon in 2019.