The sixth-ranked American came through 1-6, 6-4, 6-2 and will take on world number two and Australian Open champion Aryna Sabalenka in Saturday's championship match.
Sabalenka reached her second successive US Open final by seeing off another American, Emma Navarro 6-3, 7-6 (7/2).
"I thought I was lucky to still be in it," admitted Pegula after seeing Czech opponent Muchova miss an easy chance to go 3-0 up with a double break in the second set.
"She made me look like a beginner, she was destroying me and I was about to burst into tears but it all came down to small moments.
"I don't know how I turned that around."
Pegula has now won 15 of 16 matches on the US summer hard court swing which saw a title in Toronto and defeat in the Cincinnati final to Sabalenka.
"It's a chance for revenge, but she'll be tough to beat," said Pegula.
Muchova saved three break points in the third game of the first set which sparked a rapid collapse by Pegula.
The 30-year-old American dropped serve in the fourth and sixth games and lost a set for the first time in the tournament.
Muchova'a all-court game yielded 11 winners to her opponent's three as the opener was wrapped up in just 28 minutes.
It was a severe comedown for Pegula who had knocked out world number one Iga Swiatek on Wednesday to reach her first Grand Slam semi-final after losing all six of her previous last-eight matches.
Muchova then broke for a 2-0 lead in the second set, racking up a seventh game in a row before Pegula stopped the rot.
That suddenly reinvigorated the American who went 4-2 ahead before being pulled back to 4-4 but then levelled the semi-final when Muchova double-faulted on set point.
Pegula sprinted to a break up at 3-0 in the decider and then 5-2 after a seventh game which stretched to alnmost 10 minutes.
The last of Muchova's 46 unforced errors sealed her fate.
