World number two Swiatek, who lifted the trophy in the prestigious 1000 event in 2022 and 2024, won the last 10 games to halt Muchova's eight-match winning streak, which included her first title since 2019 in the Qatar Open last month.
"I felt I was playing better and better, just great," Swiatek said in her on-court interview.
"I love playing here, I love the conditions. I started to understand them a bit better a couple of years back and since then it feels like I can really use my advantages here.
"It's a great place to play tennis, hopefully I can keep doing that until the end."
She next faces either ninth-seeded Ukrainian Elina Svitolina or 44th-ranked Czech Katerina Siniakova, who ousted defending champion Mirra Andreeva in the third round.
In other women's matches, reigning Australian Open champion Elena Rybakina, the 2023 Indian Wells winner, faces unseeded Briton Sonay Kartal.
Fifth-seeded American Jessica Pegula takes on Swiss veteran Belinda Bencic, who has won all four of their prior encounters.