The world number one took 57 minutes to overcome the 17-year-old Australian to win 6-2 6-1.
The American, who is seeking an 18th major title, extended her winning streak to 23 matches.
"I was so ready today because she's such a good player with such a good future," said Williams.
"I would love to have a win here but there are so many tough opponents in the tournament so I have to come out and enjoy myself."
Up next for Serena is the young Serbian Vesna Dolonc in the next week.
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