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Williams mixed a high number of winners with errors against experienced Austrian Yvonne Meusburger but eventually ground her way to a 4-6 6-3 6-2 win in one hour 53 minutes.
She produced some spectacular play at times on the back of her big serve and powerful forehand against the solid Meusburger, but still hasn't found her range in her two matches of the new season so far. She will now play young Spaniard Garbine Muguruza, who beat Canada's Sharon Fichman in three sets.
Second seed Kirsten Flipkens beat Karolina Pliskova 6-4 6-3 in the first match on centre court and fifth seed Jamie Hampton was equally comfortable in dispatching Kristyna Pliskova, Karolina's twin, 6-3 6-4 in just 63 minutes.
Flipkens will take on either Julia Goerges or Sachie Ishizu in the quarter-finals and Hampton will play the winner of the match between Ana Konjuh, who ousted top seed Italian Roberta Vinci last night, and Lauren Davis.
Japan's Kurumi Nara also continued her impressive run, beating compatriot Ayumi Morita 6-0 6-1. Nara has dropped only two games so far in the tournament, although her first-round opponent Alexandra Cadantu withdrew through injury when trailing 4-0 in the second set. Nara will play either Ana Ivanovic or Johanna Larsson in tomorrow's quarter-finals.
Ana Ivanovic, the highest seed left in the tournament at No 2, is due to take on Sweden's Johanna Larsson tonight before Konjuh and Davis square off.