Relegated to the new Court 18 for the day, the Romanian had to battle for an hour to take the opening set but sped through the second with a minimum of fuss.
Petkovic, a semi-finalist in 2014 but now ranked 107, needed treatment on her right knee at the start of the second set and was no match for the twice runner-up.
Halep, cheered on by a noisy group of Romanian fans, finished it off with a clinical backhand winner.
In the fourth round, she will face 16th seed Elise Mertens, who beat Australia's last hope in the singles draw - Daria Gavrilova.
