Sharapova and Williams have 11 majors combined -- four for the Russian, and seven for Williams.
The 32-year-old Williams broke Sharapova as the Russian was serving for the victory at 6-1, 5-1 to keep the match alive. But Sharapova was able to close it out on her next service game.
Williams could consider herself fortunate -- Sharapova's opponents in her first two matches failed to win a game from the Russian star.
Williams has only advanced past the third round once in the past two years -- at Wimbledon in 2011.
Sharapova lost the 2012 Australian Open final before going on to win at the French Open.
Three matches into this tournament, and Sharapova, who pumped her arms six or seven times after she served out with an ace, has lost just four games heading into her fourth-round match against unseeded Belgian Kirsten Flipkens.
"I think when we both looked at the draw, it was a match-up we were both looking forward to," Sharapova said. "She's a tremendous athlete and a great champion."
The fifth-seeded Kerber won 6-2, 7-5 to move into the fourth round, farther than she's gone in six trips to the Australian Open.
Local organizers brought Kerber a cake onto the court immediately after the match and the crowd at Rod Laver Arena sang "Happy Birthday." She blew out the candles and said thank you to the crowd and to 17-year-old Keys.
"Madison is a great young player and it was very tough," said Kerber, a semifinalist last year at Wimbledon. "So happy I won today on my birthday!"
In the fourth round last year, Makarova beat Serena Williams and was the first of only four women to beat the powerful American in 2012. Kerber was the last.
"I'm extremely happy to be playing my best tennis from the beginning of the year," said Radwanska, who won tournaments in Auckland and Sydney before coming to Melbourne. "Hopefully I'll play on the same level the rest of the tournament."
Ivanovic surged to a 5-2 lead in the first set but lost the next three games. The 13th-ranked Ivanovic broke Jankovic to pull ahead 6-5 and won the first set with an ace.
The 25-year old Ivanovic had an easier time in the second set, wrapping it up on her second match point.
Li won the 2011 French Open just a few months after reaching at the Australian Open.
After soaring to 106 degrees on day four, the temperature dropped into the mid-70s on Friday, and light rain briefly interrupted play on some courts.
Information from The Associated Press was used in this report.