Gauff, seeded seventh, broke the Czech three times in the opening set and confidently served out the opener to love in her first WTA 1000 final appearance.
Muchova was too inconsistent on a hot day in Ohio, committing 35 unforced errors and badly missing a backhand down the line to hand Gauff the break and a 3-2 second-set lead.
The 19-year-old Gauff had some trouble getting over the finish line, failing to convert three match-point opportunities while serving at 5-2 thanks to some tentative groundstrokes.
But she did not falter on her next chance as Muchova's return landed wide, leaving Gauff to jump up and down in jubilation.
Muchova, who was ranked 235 in the world a year ago amid injury woes, will enter the world's top 10 for the first time despite the loss.
Gauff, who improved her record to 11-1 since falling in the first round of Wimbledon last month, looks poised to be a real threat when she arrives in New York for the final major of the year, which runs from August 28 to September 10.
"This is unbelievable, especially after everything I went through in the summer in Europe," Gauff said during the trophy presentation.
"I'm just happy to be here in this moment. I spent a lot of nights alone crying, trying to figure it out."
Following her early exit from Wimbledon, Gauff won the title in Washington DC and reached the quarter-finals of the Canadian Open before completing her victorious run on Sunday in a tournament in which she beat world No.1 and US Open champion Iga Swiatek for the first time.
