On a day of rising temperatures at Melbourne Park, Li crushed last year's girls' champion Ana Konjuh, 16, 6-2, 6-0 to become the first leading contender through.
And with the mercury climbing to 30 Celsius (86 Fahrenheit) and forecast to shoot past 40 Celsius on Tuesday, Li was glad to rip through the opener in just 61 minutes.
"I think it was very lucky we played today. Tomorrow will be the worse," said Li, adding that she moved her Tuesday practice to an earlier slot. "I didn't want to kill myself on the court," she said.
Top 10 men's players Stanislas Wawrinka, David Ferrer and Tomas Berdych also went through with Djokovic, the defending champion, set to headline the evening session.
Djokovic is bidding to become the first player in the Open era to win the title four times in a row, while Williams can equal Chris Evert and Martina Navratilova's haul of 18 majors.
In-form Wawrinka had it easy when Andrey Golubev retired when a set down, while Ferrer and Berdych won in straights against Alejandro Gonzalez and Aleksandr Nedovyesov respectively.
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