In her first match since losing in the finals of Cincinnati to Victoria Azarenka, the No.1-seeded Williams came out firing against Schiavone, losing just six points en route to a 6-0 first set then extending that lead to 60 40. Schiavone finally got on the board in the next game to cut the lead down to 60 41, but it was too little too late and Williams closed it out with an hour on the clock two games later, 60 61.
"I was just trying to be focused," Williams said. "When you go against a former Grand Slam champion, meaning just a year and a half ago, two years ago - she was in the finals of the French, then she won the French - it's not very easy to see your name on the draw like that, so you have to be very serious.
"She's a great competitor. I think she played really well. I think the scoreline had nothing to do with the match. I was just able to win some very key points. But it definitely wasn't very easy out there.
"We were both grunting and running and fighting."
There was a special moment early in the second set when, in between points, Schiavone went to the back of the court for a hug from one of the ballpeople. She was asked about it in her presser.
"A hug? No. I didn't need a hug in that moment. I needed a game, points - I didn't need the hug."
Schiavone was also asked in that post-match press conference her thoughts on Williams as a player.
"What I think of Serena as a player is not because she beat me 60 61 today - I always say I think she's one of the best athletes we've ever had in the world. We're speaking about some of the best, like Steffi Graf, Billie Jean King, Martina Navratilova. We're speaking about someone who is really unique.
"We all know that though. I don't really have to say it."
In turn Williams was asked about Schiavone, who has slipped down the rankings the last few years.
"You never know what can happen," Williams said. "Schiavone is extremely fit for 33. She doesn't look 33. She just had a couple of not-great results, but she's playing well. I really don't think she's ranked where she should be. There's nothing in me that doesn't think she'll be ranked higher very soon."
Williams was asked about another player from her generation - James Blake - who announced this will be his last tournament. "Just pure heart," she said. "I mean, the guy has just been a great person with a great heart. He's been through so much. Being able to even be a professional player with his back, and doing so well. We won together at Hopman Cup. He was such a great partner and great friend.
"It's just sad to see another good friend of mine that I'm not going to see on a daily basis."
Williams' next opponent is Galina Voskoboeva, who overpowered Monica Niculescu earlier in the day, 64 63. Williams beat Voskoboeva in their only previous meeting, on the clay courts of Rome last year.