The No.1-seeded Azarenka was the first to win, losing the sixth game of her match but winning all the other ones against Eleni Daniilidou, eventually cruising past the former Top 15 player, 61 60.
"I felt really good - I enjoyed the way I was so focused," Azarenka said. "It was definitely something I stepped up from my first match, just trying to stay in the zone and execute all of my shots. I was just trying to make everything happen out there today, and that's what I'm the most happy about."
Daniilidou had actually beaten Azarenka in their only previous meeting, though it was five years ago.
"Never underestimate anybody," Azarenka added. "Anybody on any given day can play an outstanding match, especially when they have nothing to lose. I was just focusing on each point out there."
Next up for Azarenka will be Jamie Hampton, who fired 24 winners to take out Thai qualifier Luksika Kumkhum in just under an hour, 61 62. Hampton has recorded her best career results in her last two WTA events, the quarterfinals of Osaka last fall and the semifinals of Auckland two weeks ago.
Hampton also has a claim to fame already this year - Agnieszka Radwanska is 11-0 without losing a set, but Hampton was the only player even to get to set point against her, doing so in the first set of their semifinal in Auckland (Hampton double faulted on that set point and fell by a 76(4) 76(3) scoreline).
The No.3-seeded Williams showed the ankle injury she suffered two days ago isn't hindering her results, beating Spanish teen Garbiñe Muguruza in the second match of the day on Rod Laver Arena, 62 60.
"I didn't feel anything today," Williams said about the ankle. "Obviously when you go out to play you're heavy on adrenaline and you're really pumped up. Usually I feel injuries after the match, but so far so good. I felt better than I ever dreamed of expecting to feel. It can only get better from here."
There was something bothering her mid-match though - her lip. "I just busted it wide open," Williams said. "I think it happens to everyone, but I've never busted it wide open like that. I was like, 'Oh no, I can't have a tooth fall out. That would be horrible.' But it's okay. It's a war wound.
"I don't know why my racquet was even in my face. I've been playing tennis far too long to hit myself. I think I was hitting a forehand. I was like, 'Come on, Serena, pull yourself together here.'"
In spite of all of the above, Williams managed to equal her personal serve speed record of 128mph during the match. "I did not expect that - I was like, 'Okay, I'm going to hit a big one, 200.' It went 207. I was like, 'Wow.' I think it's my fastest. I've hit some like 150s, but of course they're to the sky."
"Serena's a great player and a great champion," Morita said. "I just want to try my best out there.
"I've never played her, so I'll just go on the court and hope I can play well, and enjoy the match."