Playing fellow thirty-something Yvonne Meusburger for the first time, Williams looked somewhat out of sorts early on in the match - she dropped the first set and things looked deadlocked early in the second set too. But from 46 22 she broke away, winning 10 of the next 13 games to run away with it, 46 63 62.
"I think my opponent today has been playing some of the best tennis of her career," Williams said. "She was a totally different player than my first round opponent. She's a counterpuncher, really consistent and runs down balls, so it took me a little while to get that in my head and kind of change my strategy.
"Today was a lot about my winners and my errors - I made some spectacular winners and some spectacular errors! But in my head I just wanted to keep playing aggressive because that's my game."
Whether those aggressive shots are landing or not, Williams makes sure she sticks with the game plan.
"It's not easy to stay aggressive when I'm making so many mistakes, but when I stop being aggressive and start playing my opponent's game that's really when I start getting into trouble. Sometimes I just have to get the errors out of my system and my shots start landing. I just can't stop moving forward."
A completely upside down time zone, going to three sets - how is Williams feeling, energy-wise?
"I adjusted to the time really well actually, pretty much the first day, which is unheard of," Williams said. "I'm also getting a lot of rest every single day, which is really helping me in my matches so far."
There's a positive aura around Williams these days - and she's not setting any limits for herself.
"I never set limits on myself, or anyone for that matter. The most surprising thing I've learned in life is you can accomplish a lot more than you think you can if you allow yourself to do it, and if you aren't afraid or hold yourself back. With effort you can achieve so much. That goes for me and everyone."
All three seeds who took the court won in straight sets, with No.2 seed Ana Ivanovic routing Johanna Larsson in 43 minutes, 61 61; No.3 seed Kirsten Flipkens holding off Karolina Pliskova, 64 63; and No.5 seed Jamie Hampton making it past the other Pliskova twin, Kristyna Pliskova, 63 64.