Muchova, who came into the match against the 12th seed with a world ranking of 202, was understandably nervous from the outset but grew into the contest and eventually prevailed 3-6 6-4 6-4 in two hours and 27 minutes.
Muguruza, a former world number one who has triumphed at Wimbledon and the French Open, showed plenty of her Grand Slam pedigree by racing into a 5-0 lead as she appeared on course for a routine victory.
The Spaniard closed out the opener in 37 minutes and few of those watching the match unfold would have predicted what was to follow.
Muchova, playing in the main draw of a Grand Slam for the first time, quickly turned the tables at the start of the second set, evening up the contest after she opened a 3-0 lead on the back of some brave shot-making.
"It's the first match for me on such a big stadium so I was feeling nervous. Somehow I got used to it, I don't know how," the 22-year-old said in a courtside interview.
"I don't even know. I was surviving but I think the (fans) helped me a lot."
After she settled, Muchova displayed an adept ability to mix up her play, slogging it out from the baseline before picking the right moments to charge the net.
Muguruza, a traditional baseliner, tried to change her tactics to regain the initiative but Muchova kept her at bay with a selection of passing shots and lobs every time the Spaniard ventured forward.
Overall, Muchova hit eight aces and 41 winners as she rallied from a break down in the deciding set to seal victory and claim the biggest win of her career as the clock ticked past 1:00 a.m. at the Louis Armstrong Stadium.
Next up for the Czech is a third-round meeting with Australian 18th seed Ashleigh Barty.
(Reporting by Simon Jennings; Editing by John O'Brien)
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