The 24-year-old, Moscow-born but representing Kazakhstan, had a great result in the last round, beating No.10 seed Sara Errani of Italy 6-0, 6-4.
That first set was won in the minimal possible number of points – 24 – and is the first time in the modern era that anyone has recorded a so-called golden set at a Grand Slam.
“She’s such a solid player. I look forward to it. Hopefully I’ll be able to win a point in the first set,” said Williams, who knows she will have to improve after being taken to three tough sets against China’s Jie Zheng on Saturday. “I have to make sure I do better. Usually I return well but I hit so many errors off my returns against Zheng.”
Williams and Shvedova are first on Court No.2 and if Williams prevails she will meet either defending champion Petra Kvitova or 24th seed Francesca Schiavone in the quarter-finals. Schiavone’s fellow Italian Roberta Vinci meets Tamira Paszek of Austria, with the winner going on to play the victor in the battle of the two former No.1s, Ana Ivanovic and Victoria Azarenka.