The No.7-seeded Sharapova had more unforced errors, 17 to 15, but more than made up for it in the winners department, 17 to 4, to make it past Russian qualifier Ksenia Pervak in straights, 6-1, 6-2.
"Going into a first round match at a Grand Slam, you want to be solid and do the things you need to do," Sharapova said. "It's never easy, no matter how good you're feeling or how bad you're feeling. It's just a different story once you get on the court. And I thought I did what I had to do very well. There are things I can improve on and do better for the next match, but it's definitely nice to get through."
Sharapova was asked about the potential quarterfinal against fellow Career Grand Slam holder and WTA legend Serena Williams, which is still three victories away - and she gave the perfect answer.
"It's tough to think about that match down the line when you have to compete in three more matches before that," Sharapova said. "Obviously it's a match that many people always look forward to.
"But in many ways, it doesn't matter if it's fourth round or quarterfinal, semis, final - at a certain point, there's only one champion at a tournament. So it's not really about when you face somebody.
"And right now it's not our concern, because the next match I'm playing against Pironkova."
Sharapova has now won 48 of her last 52 matches on clay, a stretch that dates back three years.
The other Top 16 seeds in action all advanced, with No.5 seed Petra Kvitova squeaking out a tight first set then cruising against Zarina Diyas, 7-5, 6-2, No.9 seed Dominika Cibulkova beating Virginie Razzano, 7-5, 6-0, No.12 seed Flavia Pennetta beating Patricia Mayr-Achleitner, 6-2, 6-2, and No.16 seed Sabine Lisicki beating French wildcard Fiona Ferro, the youngest player in the draw, 6-1, 7-5.
Stosur, who blasted 18 winners to just 10 unforced errors to beat Strasbourg winner Monica Puig, 6-1, 6-1, was wearing some pretty heavy wrapping on her left leg - she was asked about it afterwards.
"I actually had an accident in the gym on Wednesday night and cut my leg pretty bad. I was doing some box jumps, and I missed it and landed straight on my leg, on the edge. I've got stitches - five.
"But I took two days off and then I hit late on the third day, and since I started hitting there's been no problem," Stosur added. "And I can't feel anything when I'm playing, thankfully. The stitches are fine. It's healing well. It all looks a lot more padded and everything, just simply because I obviously don't want to affect anything and hit myself or just do anything silly, and, yeah, have it hurt again."