A series of unforced errors and a double fault saw Gauff lose serve in a one-sided first set early on, and she hit a forehand when given the chance to break back.
More misses on her forehand gave Muchova the advantage at the double break, and the Czech consistently maintained her level and played out the first set with an ace.
After taking a toilet break before the second set, an invigorated Gauff returned with more aggression and eventually found a way past Muchova on her ninth break point with a superb backhand winner.
The momentum continued and Gauff cruised through the next four games to force a deciding set to the delight of the crowd, most of whom appeared to be in favor of seventh place.
Tensions grew as the third set unfolded and the pair entertained the 15,000-strong center court crowd with high-quality groundstrokes and sensational quick play in front of the net.
It was only fitting then that the match was decided in a tie-break and with the score at 4-1, Gauff somehow found a way to move to 6-6.
The twists continued when Muchova was booked for a time violation at 8-8 on serve – and she immediately fired from long range to hand Gauff the first match point.
But the crowd gasped in pain when Gauff, approaching the goal, sent the ball into the tape.
To add drama, Muchova slipped when she had a chance to convert her first match point, and Gauff produced a clean cross-court winner to cling to.
But the young American was unable to save the next ball, firing a low forehand into the net after an incredible two hours and 35 minutes.
Muchawa, who clutched her ankle and gesticulated in pain during the final set, looked exhausted as she raised her arms in celebration.
A wrist injury kept her out of action for almost 10 months from September 2023, but in those two weeks she regained her best form and beat three former Grand Slam champions en route to the final.