Serena Williams returns a winner in Stanford

The world number one had not featured on tour since her disastrous Wimbledon campaign, which saw her ousted in the third round of the singles, before illness forced her to retire from the doubles tournament.

Williams, the top seed in Stanford, allayed fans' fears for her health with a 7-5 6-2 victory over Czech Pliskova.

There were some very early concerns for Williams, as she was down 15-40 in her opening service game.

However, Williams went on to hold, and allow Pliskova only one more break-point chance for the encounter as she got into her serving groove.

The 17-time major winner sent down nine aces, although Pliskova was not completely outclassed.

The 22-year-old did not concede a break-point chance until the 12th game of the first set, in which Williams managed a break to love to avoid a tie-break.

That seemed to dent Pliskova's confidence, who again could not get a point on her own serve in the second game of the second set as Williams took a stronghold on the contest.

A third break-to-love for the contest sealed Williams' progression to the quarter-finals, where she is set to meet either Serbia's Ana Ivanovic or Canada's Carol Zhao.

Earlier, second seed Agnieszka Radwanska was upset by Varvara Lepchenko 6-3 3-6 6-4.

The world number five, and 2013 finalist, was broken six times for the encounter, as the 59th-ranked American caused a boil over.

Eighth seed Andrea Petkovic negotiated her encounter with Japanese qualifier Naomi Osaka well, winning 6-2 6-2.

American qualifier Sachia Vickery continued her impressive run at the WTA Premier tournament, fighting back to beat Puerto Rico's Monica Puig 6-7 (4-7) 6-2 6-1.