The American top seed, vying for a sixth Australian title and the first since 2010, was slow to get in the groove against 26th-ranked Ukrainian Elina Svitolina, going down 6-4 in the first set.
But she shook off the cobwebs under the blazing sun on Rod Laver Arena to rattle through the next two sets 6-2, 6-0.
It keeps alive her quest to add a 19th Grand Slam title, which would take her to clear second on the all-time Open Era Grand Slam winners list.
"When in doubt just start running as fast as you can, that's what Venus always told me, that helped," said Williams, whose world number one ranking is on the line if she fails to win the tournament.
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She added that her sister's late-career renaissance was an inspiration.
"She's winning, she's doing so well and I can do better. We always motivate each other. I'm so proud of her and we're so excited."
Fellow world number one Novak Djokovic plays later today, with the Serb's chances of a fifth Australian crown improving after Roger Federer's shock exit yesterday.
Wawrinka, who beat Rafael Nadal in the final last year, could meet Djokovic in the semi-finals and stayed on track with a 6-4, 6-2, 6-4 drubbing of Finland's Jarkko Nieminen.
The Swiss, who was always in control, was pleased with his progress so far.
"It's been three really good matches, I think my game is there and I'm really happy to get through again," said Wawrinka, who will next meet Spain's Guillermo Garcia-Lopez.
Eighth seed Canadian Milos Raonic also went through, sweeping aside Germany's Benjamin Becker in straight sets.