The 27-year-old Russian had been in danger of becoming the most famous victim of qualifier Alexandra Panova's career before she banged out four booming forehand winners to stave off defeat at 5-4 down in the third set.
She then romped through her own service game to love with two aces before breaking to clinch a 6-1 4-6 7-5 victory over the 150th-ranked Panova that set up a clash against either Kazakhstan's Zarina Diyas or Slovakia's Anna Schmiedlova.
"I was dwelling too much on my mistakes, what I was doing wrong, not really being in the present, something that I'm really usually good at," Sharapova told reporters.
"At that point when you're behind and you feel like you're making a lot of errors, you don't feel like you have a good rhythm, I just really tried to take it a point at a time, think positively and change my thought process.
"When other things aren't working, maybe the mental side of things will help you out.
"I think in the end maybe that's what did."
The second seed arrived at Melbourne Park in good form having won the Brisbane warmup event and carried her momentum forward with a comfortable first round victory over Petra Martic.
She had also not lost to an opponent ranked lower than 150 at a grand slam since Alla Kudrytseva beat her at Wimbledon in 2011 and appeared to be in no mood to repeat the experience on Wednesday with air temperatures nudging 32 degrees Celsius.
The five-times grand slam winner raced through the first set in 26 minutes, winning two service games to love and breaking her Russian compatriot three times, but the 25-year-old Panova somehow clawed her way back.
Panova, whose opening round win over Sorana Cirstea was her first in a grand slam main draw, took a 5-2 lead in the second before Sharapova battled back and had a chance to level it, but her opponent held her nerve to send the match to a deciding set.
Sharapova took an extended break between sets but grew more agitated as Panova seized a 2-0 lead, and then earned two match points serving at 5-4 before Sharapova escaped.
"She came up with a good shots, with the winners. What could I do?" Panova said. "She's a great fighter. She's a great champion. To take it from her, you really need something extra."
(Reporting by Greg Stutchbury; Editing by John O'Brien/Peter Rutherford)
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