The match started brightly for the 22-year-old German, who claimed a late break of Cirstea's serve to take the opening set 6-4.
However, Romania's Cirstea, currently ranked 38th in the world, responded positively to going behind.
Having broke Lisicki's serve early in the second set, she forced a decider with another break which resulted in a 6-2 success.
Heavy rain showers then forced a two-hour delay, but when the duo returned to the court Cirstea soon built up a 3-0 lead.
She continued to dominate the encounter thereafter and eventually ran out a 6-2 winner in the decider.
Cirstea will now face either Anna Tatishvili for a slot in round three.