A pumped-up Azarenka, with her renowned grunting at full volume, said her game was exactly where she wanted it after crushing Greece’s Eleni Daniilidou 6-1, 6-0.
She was followed onto Rod Laver Arena on a scorching hot day by Williams, with all eyes on her condition after a nasty roll of the right ankle in her first-round match.
But the American third seed, looking for a sixth Australian title, was moving freely in a solid 6-2, 6-0 workout against Spanish teenager Garbine Muguruza.
“It’s feeling better,” she said of the heavily strapped ankle, which needed intensive treatment over the past two days.
“I did everything I could, from icing to massage, and woke up this morning and it was like ‘my God, it feels good.’”
The 15-time Grand Slam winner, who has admitted she’s eyeing the first calendar-year Grand Slam since 1988, next plays Japan’s Ayumi Morita, who beat German Annika Beck 6-2, 6-0.
Williams had never played the 112th-ranked Spaniard, who was making her tournament debut, and she raced to a 2-0 lead before some uncharacteristic forehand errors allowed Muguruza to hold serve and get off the mark.
She wasn’t at her best and even hit herself in the face with her racquet in the sixth game as she went for a lob at full stretch, spending the next game dabbing at her lip.
But she rallied to break once more for 5-2 and held for the set.
The second set opened with a marathon 18-minute game, with Williams finally prevailing to break. “One day I twist my ankle and then today I hit myself in the face. I don’t know what’s going to happen on Saturday,” she joked afterwards.
Former world number one Caroline Wozniacki also progressed, beating Croat Donna Vekic 6-1, 6-4, but eighth seed Petra Kvitova, the 2011 Wimbledon champion, crashed out to Britain’s Laura Robson, 2-6, 6-3, 11-9.
Meanwhile, Japan’s Kimiko Date-Krumm, 42, became the oldest player to make a Grand Slam third round since Renee Richards in 1979.
In other games, Italian 16th seed Roberta Vinci beat Uzbek Akgul Amanmuradova and 14th seeded Russian Maria Kirilenko ousted Chinese hope Peng Shuai.
Azarenka next faces American Jamie Hampton, who sent Thai qualifier Luksika Kumkhum packing 6-1, 6-2, and said she felt in good touch.
“I felt really good, I enjoyed a lot the way I was focused,” she said.
“I definitely stepped it up from my first match, and I was in the zone trying to execute all of my shots. I was trying to make everything happen, and that’s what I’m happy about.”
Azarenka had only played the Greek once before, five years ago, and lost, but opened her account by breaking to love and then comfortably held.