The prospect of an all-American final had already been scotched when Belarusian Sabalenka earlier downed Emma Navarro 6-3, 7-6(2) and for a while in the later match, it looked like the host nation would be unrepresented in the title decider.
Playing in her first major semi-final, Pegula was made to look like a novice by Muchova in a disastrous opening set but somehow turned the tables on the unseeded Czech.
Pegula could only muster up three winners across the first set as Muchova showed no signs of rust despite her recent return from a wrist injury that sidelined her for some 10 months.
With the famously raucous main showcourt deathly quiet, the Czech looked as though she might roll through the rest of the match after going 2-0 up in the second set.
Pegula, though, gradually found the form that had seen her win 14 of her previous 15 matches to break her opponent in the fourth game and again in the sixth.
"It comes down to really small moments that flip momentum," said Pegula.
"She made me look like a beginner... I was about to burst into tears because it was embarrassing.
"I started to play like how I wanted to play... It took a while but I don't know how I turned that around, honestly."
Muchova broke back in the seventh game but the mistakes were piling up and she showed her nerves by double-faulting on set point to give Pegula an opening she did not pass up.
Roared on by the crowd, Pegula marched through the first three games of a near-flawless final set and threw her hands in the air in delight after breaking Muchova on her second match point with a fine forehand return.
