The 2008 champion has lost five games in reaching the fourth round at Melbourne Park. She won her first two matches 6-0, 6-1 despite not playing any warmup tournaments because of an ankle injury.
Second-seeded Petra Kvitova took an easier path into the Round of 16 when Maria Kirilenko retired with a left thigh injury while trailing 6-0, 1-0 after 38 minutes in their third-round match.
Former finalist Jo-Wilfried Tsonga hardly broke sweat, either, in a commanding 6-2, 6-2, 6-2 win over Frederico Gil of Portugal on the men's side.
The scoreline on Saturday made it look easy enough for Sharapova, but she was full workout in a 56-minute second set, with many games going to deuce.
After clinching the victory with a forehand winner, Sharapova showed her relief by clenching her fist and screeching "come on."
"She certainly stepped up in the second set," Sharapova said. "She reached the semifinals at the U.S. Open last year so she's been on the big stage before and I knew she could produce some really good tennis."
Sharapova and Kvitova both have a chance of claiming the No. 1 ranking at the end of the tournament. They could play each other in the semifinals, although Kvitova insisted she hasn't looked that far ahead.
"I don't know who lost and who win," the Wimbledon champion said. "No, really, for me doesn't care."
Kirilenko had treatment for her injury during the first set against Kvitova and, after dropping serve immediately in the second, she walked to the net and shook hands with Kvitova.
It was the fourth retirement of the women's tournament.
Kvitova will face Ana Ivanovic of Serbia or unseeded American Vania King in the Round of 16.
King and Serena Williams are the only American players left in the singles draws after John Isner's loss on Friday ended any hope of a men's champion from the United States.
Five-time champion Williams, hoping to win her 17th straight match at Melbourne Park, was up against Greta Arn of Hungary in a later match Saturday.
No. 1-ranked Novak Djokovic and No. 4-ranked Andy Murray were both up against French opponents in Nicolas Mahut and Michael Llodra.
In all, six Frenchmen reached the third round. Tsonga wasted hardly any time becoming the first of them to move into the Round of 16.
The 2008 finalist took six of his seven breakpoint opportunities and saved all five against him.
"I had to take it seriously and this is what I did. I'm just really happy to go through," said Tsonga, who will face fellow Frenchman Julien Benneteau or Kei Nishikori of Japan next.
There will be no U.S. player in the men's fourth round at the Australian Open for the first time since 1973 — when no Americans travelled to the tournament.