Williams will play either second-seeded Victoria Azarenka or unseeded Tamira Paszek, who were to play later in the afternoon.
Much to her consternation, Williams has not captured a Grand Slam title since winning Wimbledon in 2010, and her suspect baseline play and sloppy footwork have fueled skepticism that this would be the tournament to snap that streak.
But unlike in her previous two matches — both struggles, both tense three-set duels — Williams often dictated points against Kvitova, often on the strength of her serve and service return. Williams ripped 13 aces against Kvitova, running her total to a tournament-leading 61.
Williams’s early dominance in the first set, in which she recorded 17 winners and only four unforced errors, gave way to a taut second set featuring the best of grass-court tennis — aggressive play, big serves and brief, but intense, rallies.
Serving at 5-5, 30-0, Kvitova committed four consecutive mistakes to cede the break to Williams. Serving for the match, Williams blasted three aces and on match point clobbered a 116-miles-per-hour serve out wide that grazed Kvitova’s racket frame.
There were no leaps of celebration from Williams after this victory, no exultations of joy. It was a much more subdued reaction, perhaps in part because Williams did not fight herself as much Tuesday. She seemed in control from the outset, even as she traded service games with Kvitova in the second set.