Her reliable runs are especially impressive given the current depth in the women’s game, compared with early in her career, when wins in the opening rounds were often routine.

“Now I’ll play players who I’ve never seen or know their name, and you can’t let up one point,” Williams said.

Suárez Navarro, a tenacious Spaniard with a fluid one-handed backhand, was a known quantity for Williams, having won three of their previous seven matches.

“I was happy about this match because she wasn’t seeded here, but obviously, she knows how to play,” the ninth-seeded Williams said of Suárez Navarro. “She’s played deep in the majors. She’s won big titles. This was my best match, so I was happy to see my level rise as the tournament is continuing, because I know my opponents are going to be better; I need to be better. To be able to be out there and execute things that I wanted, it was a good feeling.”

Williams’s opponent in Tuesday’s quarterfinals is No. 13-seeded Petra Kvitova, who is also having a remarkable season — for a significantly different reason.