Williams is also used to her opponents raising their games - Parmentier didn't look like the world No70, who has never progressed beyond the fourth round of a grand slam - and the 35-year-old Williams showed her ability to fight, which is often underestimated. She only landed 48 per cent of her first serves, but saved eight of 10 break point opportunities.
"You always feel rusty going out there in your first match," said Williams. "I feel that rust but mentally I felt like I knew how to get it back, I knew how to get in there and that felt really good."
The American also had good vibrations about the crowd reception, which, even by Auckland's high standards, was quite exceptional. Williams was welcomed and farewelled by a standing ovation, with the crowd taking her to their hearts from the outset.
"It's my first time in New Zealand so to get that reception was really amazing," said Williams. "I was talking with my team afterwards; wow what a wonderful feeling, to still be able to play all these years later and still have that reception is great."
Williams gave a patchy display on Tuesday, but there were plenty of moments to remind why she owns 22 grand slams, and counting. A couple of groundstrokes were hit with such ferocity that they seemed to pass straight through Parmentier's racquet, as the French player swung at fresh air. Some of her serves and returns were simply vicious, and a half volley played off her toes near the baseline was sumptuous.
And the good news? There is a discernible hunger, even after all she has achieved, to get better.
"I want to improve...I don't just want to have the same game," said Williams. "We definitely worked on a few things that we want to improve on and hopefully you'll be able to tell me in the next couple of months."
Williams is back on court on Wednesday, against compatriot Madison Brengle. Their only previous meeting was a 6-1 6-0 win to Williams on clay in 2015, and a similar score line wouldn't surprise today as the world No2 gets into her work.