Williams, the eighth-ranked racquet in the world, scored five breaks on eight occasions compared to one-of-a-kind (five break points) for Muchova, who was 44th. The American, who turns 38 in September, also had the upper hand on winning shots, 20 against 17, and direct fouls, 15 against 22.
In the round of 16, the one who won 23 titles in Grand Slam tournaments will be opposed to the Croatian Petra Martic. The 22nd seeded Latvia's Anastasija Sevastova, ranked 12th, 6-4, 6-3, was right.
In the other matches, the third seed Karolina Pliskova ignored a run in the second set to win 6-1, 4-6, 6-4 at the expense of Ons Jabeur.
After Jabeur had asked for a healer after the first run, she regained her grip and Pliskova was overcome with frustration, even smashing her racket on the ground, which resulted in a formal warning from the official.
Jabeur, a Tunisian who was trying to become the first Arab to reach the fourth round of a major tournament, however missed pace in the final round. Although she scored 49 winners in that match, she also committed 43 unforced errors, including 17 in the third set.
"She played a lot better from the 2nd set and scored incredible points," said Pliskova of his opponent to explain his own difficulties.
"I had to serve well to get by and especially save break points," she said.
Pliskova will be opposed in the round of 16 to the Briton Johanna Konta. The 16th seed placed Shuai Zhang, ranked 33rd, 6-2, 6-3.
The second world racket, the Australian Ashleigh Barty, also reached the round of 16 when she showed the exit to the Greek ranked 30th Maria Sakkari 7-5, 6-3. Barty is waiting for the winner of the match between Qian Wang (18th) and Fiona Ferro.
Madison Keys defeated Sofia Kenin in an American duel, 6-3, 7-5. Elina Svitolina won the battle of Ukraine, 6-2 and 6-0 against Dayana Yastremska. Both are from Odessa.
Keys will be opposed to Svitolina in the next round.
Andreescu eliminated in duplicate
In doubles, Bianca Andreescu and Sharon Fichman lost to Americans Whitney Osuigwe and Taylor Townsend 6-2, 6-3, while Gabriela Dabrowski and Yifan Xu, seeded third, went on to defeat Lidziya Marozava and Katarina Srebotnik 7-5, 6-4.
Dabrowski will also play the mixed doubles later in the evening. Her partner, Croatian Mate Pavic, and her, ranked second, will face Croatian Darija Jurak and New Zealander Marcus Daniell.