She broke again for a 5-0 lead and sealed the set in 24 minutes, with Muchova winning only 11 points, hitting just one victor against 13 unforced errors.
Barty then went behind a break in the first game of the deciding set and was unable to regain ground or her composure, falling to the Czech in one hour and 58 minutes.
"Ash started very good, she played nearly like no mistakes, it was very tough".
"I started feeling a bit lost", Muchova said. She played like no mistakes.
She left the court at the first changeover of the second set for a medical time out and confirmed after the match that she didn't receive treatment for the abdominal injury which saw her pull out of the Gippsland Trophy a fortnight ago.
Muchova's 1-6, 6-3 and 6-2 victory sets up a semifinal against the victor of the all American clash between 22nd seed Jennifer Brady and the unseeded Jessica Pegula. I was a bit lost on the court and my head was spinning, so I took a break.
It was an error-riddled second set for Barty, who made 19 unforced errors and landed just 52 per cent of first serves. "And it helped me". Medical personnel took her pulse and temperature before she left the court, and when the Czech returned, she played much better.
'It's taken us, Casey and I have been chatting, taken us a few minutes to try and process and think, really think about what actually happened there, ' Smith said afterwards.
Muchova said she'd then tried to play more aggressively against Barty and utilise more of an all-court game. Upon returning, Muchova won six of the next seven games to take the set and force a third.
Muchova's only other victory over a top-five was against No. 3 Karolina Pliskova at Wimbledon in 2019. Barty finished with 37 unforced errors and lost serve four times in the final two sets.