The American teenager, 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, who will enter into the top 10 for the first time thanks for her run to the final, was too inconsistent on a hot day in Ohio, badly missing a backhand up the line to hand Gauff the break and a 3-2 second-set lead.
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 on her next chance to serve for the title she did not falter, Muchova's return landing wide as Gauff jumped up and down in jubilation.
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 28th-September 10th.
"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."
She will be seeded sixth at Flushing Meadows after winning the title in Washington DC, making the quarters of the Canadian Open and winning the title on Sunday in a tournament where she beat world number one and US Open defending champion Iga Swiatek in the semis.
