Now seeded 14th, Djokovic needed four match points in an eight-minute last game before clinching the win against Mofils, who needed a medical time out for heat stress in the second set and said he had trouble breathing.
Considered one of the contenders for the title after Serena Williams opted against defending her Australian title, Muguruza had a troubled preparation including a retirement at the Brisbane International and a withdrawal ahead the quarterfinals in Sydney because of a right thigh injury. The 2016 victor from Germany and 21st seed roared past the unseeded Russian 2008 champion 6-1, 6-3 in 64 minutes to reach the last 16.
But her first serve was a liability on Saturday night, when she put just 38 percent into play.
The world No.1 edged past an inspired Davis 4-6 6-4 15-13 in a thrilling marathon encounter which lasted 3 hours, 44 minutes and 58 seconds to advance to the fourth round at the Melboure Park.
Sharapova hit 10 of her 15 winners in the second set but a ruthless Kerber maintained the advantage to consign the Russian to her worst result at Melbourne Park since 2010.
"She never really lets up and she gets a lot of balls back and that's something I've had trouble with in the previous matches against her", said Sharapova, who dominated the winners' count 30-6. "I have some figuring out to do, what happens to me in deciding moments in Grand Slam", he said.
Djokovic goes forward to a third-round meeting with 21st seed Albert Ramos-Vinolas after the Spaniard defeated Tim Smyczek from America 6-4 6-2 7-6 (7-2).
World No 1 Simona Halep saved three match points to survive a titanic struggle and make the last 16 at the Australian Open Saturday where she joined Karolina Pliskova and Caroline Garcia.
"I just have to accept it, embrace it, obviously hope for a better day next match". "Everybody who knows me knows I never give up, I always come back", she said. No. 20 Barbora Strycova beat U.S. qualifier Bernarda Pera 6-2, 6-2, leaving U.S. Open finalist Madison Keys as the only American woman to reach the fourth round. It's a lot of things that take time.
Kerber has started this year well, though, and was in imperious form to defeat Sharapova 6-1 6-3 on Rod Laver Arena.
Another loss at a major had the highly-touted Zverev admitting he may have a problem.
Ottawa's Gabriela Dabrowski moved on in mixed doubles.