The 23-time grand slam champion had to deal with the hype of a first-round meeting with Maria Sharapova, and then dropped a set in a dramatic second-round encounter with 17-year-old Caty McNally.
However, Williams was able to see off Czech Karolina Muchova 6-3 6-2 with a minimum of fuss on Arthur Ashe.
"Yeah, I had to go out there on business," she said. "I think I tried to do that with all three matches thus far.
"It was just different because I know that she could play today. I knew what she could do.
"I don't know how I would grade my performance. I've just got to keep playing and believing."
Williams plays Petra Martic of Croatia, the 22nd seed, in the fourth round.
She can put her feet up on Saturday and join the rest of the United States in watching the eagerly-anticipated showdown between defending champion Naomi Osaka, 21, and 15-year-old sensation Coco Gauff.
"I think it will be a really interesting match. I definitely am interested to watch," Williams said.
"What do I make of it? I don't know. I think it's super-exciting tennis. Coco is obviously much, much younger than Naomi, if you could say that, because Naomi is incredibly young.
"But it's shocking to say that Coco is about six years younger.
"I definitely think it's the future of women's tennis. And I'm really excited to just be a fan girl and kind of watch."
Second seed Ashleigh Barty was also a straight-sets winner against Maria Sakkari of Greece.
Karolina Pliskova, the third seed, needed three sets to beat Ons Jabeur of Tunisia and set up a clash with Britain's Johanna Konta.