The former world number one got off to a bright start, claiming the first three games of the opening set and looking likely to sweep through the initial stages of the match, until Lisicki made herself known and drew level at 3-3.
Despite starting positively, Sharapova failed to overcome her German opponent, who managed to break the fourth seed and take the lead in Melbourne.
While the second set started evenly, with each game going by the way of serve, Sharapova clinched the breakthrough in a bid to draw level on sets and stay in the competition.
The Russian pro held on to her lead and prevented herself from relinquishing the game by leveling the score heading into the third set.
The competitors continued to be well-matched in the opening stages of the final set. However, Sharapova slightly edged the contest and claimed the match.
The 24-year-old will face Ekaterina Makarova in the quarter-final following her victory over Serena Williams.