Defending men's champion Stan Wawrinka, Japanese fifth seed Kei Nishikori and women's fourth seed Petra Kvitova also stayed on course.
Eighteen-time Grand Slam winner Williams opened her Melbourne Park account with a decisive 6-0, 6-4 display against Belgium's Alison Van Uytvanck, laying down the marker to her challengers.
A sixth Australian Open title would take her to clear second on the Grand Slam Open Era winners list behind Steffi Graf's 22, having joined Chris Evert and Martina Navratilova on 18 with her win at the US Open last year.
Serbian top seed Djokovic, gunning for a fifth Australian title, also found his groove early against Slovenia's Aljaz Bedene to post a commanding 6-3, 6-2, 6-4 win.
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"For a first round performance it was pretty good, obviously I still need to work on a few things, I'm still developing my game," said Djokovic, who lost to Wawrinka in the quarter-finals last year.
The Swiss fourth seed went on to stun Rafael Nadal and win his maiden Grand Slam, and he is keen to repeat the heroics again this year.
"It was great to be back on Rod Laver Arena again, it brings back so many memories from last year," he said.
"It was such an amazing two weeks last year so it was great to come back here and I am pleased with my game in general and I'm excited to start again."
Roger Federer, Nadal and Maria Sharapova all played Monday and easily progressed.
Nishikori, who lost to Marin Cilic in last year's US Open final and is touted as a future major champion, showed his mettle to beat Nicolas Almagro 6-4, 7-6 (7/1), 6-2.