Sharapova was playing Down Under for the first time since she tested positive for meldonium two years ago.
Despite the absence, she looked as sharp as ever when breaking serve in the second game to storm into a commanding position.
Maria, the underdog despite being ranked one position higher in the ATP World rankings at 46th, responded brilliantly with a break of her own in the third.
But again the Russian bounced back by taking the fourth game to lead 3-1.
From there the first set was wrapped up routinely by Sharapova as she cruised to a 6-1 win.
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Maria started the second set the brightest by breaking in the second game before taking a 3-1 lead.
But Sharapova showed why she used to be the top player in the world by winning the next four games to put herself within one game of victory.
The German then surprisingly held serve in the ninth to give herself a glimmer of hope with the score at 5-4.
But Sharapova proved too powerful as she served for the match and hit an ace to book her place in the second round with a 6-1 6-4 win.