Sharapova, who also beat the German in the Wimbledon semi-finals last year, prevailed 3-6 6-2 6-3.
It seemed plain sailing for the fourth seed when she coasted into a 3-0 lead only for Lisicki to hit back to win six games in a row and take the first set.
Sharapova refocused and started to get the better of some hard-hitting baseline rallies as her opponent's belief started to wane.
She levelled it up and then stood firm on the big points to advance in two hours and 15 minutes.
"There were a lot of ups and downs tonight [Monday] but fortunately I finished on a high note," said Sharapova.
"She's such a good opponent, she has such a big game and even though I didn't play my best tennis tonight [Monday] I fought until the end and that got me through."
Next up for Sharapova is compatriot Ekaterina Makarova, who claimed the scalp of Serena Williams earlier on Monday.