For the first time, it appeared she fully understood what she meant to the sport -- and what it meant to her.
"She was beyond everyone as far as athleticism and power," Evert said. "The question was all the other stuff. She went through five, six years where she was in and out of the game, distracted or injured. Tragedies in her life, going through so much adversity. It's beautiful to see her come outside the other end because she deserves it. She deserves to break my record and Martina's."
After losing to Williams in last year's US Open final (6-1 in the third set), Azarenka -- eight years her junior -- was asked if she thought Williams could catch Graf's 22 majors.
"Well, it's not something I'm really thinking about, to be honest," Azarenka said, smiling graciously. "But I think it's incredible what she's achieving. She's playing definitely her best tennis right now.
"That's just really exciting for me to be able to compete against that type of player who can be the greatest of all time."
There is a widespread feeling that Federer will finish with his present total of 17 Grand Slam singles titles. How many will Williams wind up with?
"She's got a lot of tennis left in her," Graf told The AP. "I can easily see her pass all of our records. I don't see the competition catching up to her at all.
"We'll see how mentally and physically she's able to preserve herself over the next few years. I don't think anybody's ever played that far, that kind of tennis, at her age. I'll be curious to follow her."
Like Graf's husband, Andre Agassi, Williams took a number of mental and physical sabbaticals during her career. This allowed Agassi -- who finally realized he was squandering his great gift -- to summon the fire to compete late in his career. The same thing seems to have happened to Williams.
"There is a finish line," Gimelstob points out, "but hopefully not for a very long time. A healthy, focused and motivated Serena is virtually unbeatable. At the end of the day, her consistency won't have matched Chrissie or Martina or Steffi, but her record in the biggest moments will be her legacy.
"Setting a line in Vegas, I'd put the over-under at 20 -- and take the over. I'd take four and be surprised if she isn't into the low 20s. Steffi's 22 is very plausible."
Davenport isn't sure. Awaiting the imminent birth of her fourth child, she won't be in Australia but will work Indian Wells and the French Open as a Tennis Channel analyst.
"I'd say definitely 20, and then we'll see," Davenport said. "The only concern is injuries. She wants it so badly. She won't burn out. Last year, for the first time in a long time, she played a full schedule. She fought through it. The team will have to take a look at that.
"I think she has four left in her. … That's what my head tells me now. After she wins in Australia, we can chat again."
Making it happen
It helps to have a killer instinct.
In the crucible of a Grand Slam final, only Court was better in Open era competition. The Australian was 11-1 (.917) in major finals, and Williams isn't far behind at 17-4 (.810). By comparison, Navratilova and Evert were 18-14 (.562) and 18-16 (.530), respectively.
At least in her public pronouncements, Williams has seemed, well, almost humble.