As temperatures soared and big names fell by the wayside, Djokovic and Williams dodged the day-time heat to open their campaigns with wins on a balmy evening at Rod Laver Arena.
Williams put Australian teenager Ashleigh Barty to the sword but Djokovic, playing his first competitive match under new coach Becker, was surprisingly sloppy as he took nearly two hours to subdue Slovakia's Lukas Lacko.
"It's my first competitive match this season after a five to six week break and I was rusty in the first two sets," admitted the Serb, seeking a fourth straight Melbourne title.
Despite the relatively below-par 6-3, 7-6 (7/2), 6-1 win, Djokovic was in no danger of joining Petra Kvitova, Venus Williams and Sara Errani among the casualties on day one.
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The unseeded Venus Williams, wilting in the midday heat, lost to Russia's Ekaterina Makarova over three sets while Italian seventh seed Errani went out to Julia Goerges.
And former Wimbledon champion Petra Kvitova, the sixth seed, fell victim to a sensational upset when she was ambushed 6-2, 1-6, 6-4 by unheralded Thai Luksika Kumkhum.
"I think that probably I wanted it too much, and then everything just fell down," said the crestfallen Czech.
"I think it was very lucky we played today. Tomorrow will be the worse," said Li, adding that she moved her practice on Tuesday, when temperatures are forecast to soar, to an earlier slot. "I didn't want to kill myself on the court," she said.