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.
Meanwhile, Fifth-seeded American Jessica Pegula beat Belinda Bencic 6-3, 7-6(5) to advance, claiming her first victory over the Swiss veteran after four defeats.
Up 5-3 in the second set, Pegula thwarted a late comeback bid from Bencic, who produced a love service game then broke Pegula as she served for the match at 5-4.
Bencic then held serve to force the tiebreaker, saving a pair of match points before Pegula closed out the win on her third opportunity.
"She made me have to earn it today," Pegula said.
"I felt like in the second set, when I got up there, I had a little bit of a lull where I had a couple of game points and I could have maybe finished the match.
"But she's a really good player and when you don't quite finish those off that's where she can come in, and that's what she did."
Pegula will next face either reigning Australian Open champion Elena Rybakina, the 2023 Indian Wells winner, or unseeded Briton Sonay Kartal.
