The American, with a record 23rd major title in her sights and watched by her new fiance, Reddit co-founder Alexis Ohanian, thumped dangerous Swiss teen Belinda Bencic 6-4, 6-3.
Williams has barely played since her shock defeat in the US Open semi-finals in September and she made, by one count, 88 unforced errors in her second-round loss to Madison Brengle at this month's Auckland Classic.
But she came through a tight first set against Bencic before dominating the second set in what turned out to be a convincing victory on the centre court.
"Right now I've got nothing to lose. Every match, every tournament I'm playing for fun," she added.
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Williams, who can break Steffi Graf's Open-era record of 22 Grand Slam titles if she wins in Melbourne for the seventh time, next faces Lucie Safarova, who had a charmed life in her win over Yanina Wickmayer.
The Czech survived nine match points before winning 3-6, 7-6 (9/7), 6-1 against the flummoxed Wickmayer, who said she was feeling "definitely not good" after letting slip so many opportunities.
"But I think it's normal when you have match point and you want to play it a little bit safe. Then after, you realise it's not the best option."
Men's world number three Milos Raonic, a semi-finalist last year, enjoyed an uncomplicated start to his campaign when he beat Germany's Dustin Brown 6-3, 6-4, 6-2.
And German hotshot Alexander Zverev credited a racquet-smashing tantrum with sparking his revival as he came back to beat Robin Haase 6-2, 3-6, 5-7, 6-3, 6-2.
Women's fifth seed Karolina Pliskova, whose win over Williams at the US Open ended her 186-week stint as world number one, smashed Spain's Sara Sorribes Tormo 6-2, 6-0.
And Britain's Jo Konta, riding high after her victory at last week's Sydney International, beat experienced Belgian Kirsten Flipkens 7-5, 6-2 to reach the second round.
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