The 98th-ranked Petkovic has won eight titles on the lower ranked ITF circuit, but had never before reached a WTA quarterfinal.
"I was hoping to land my first title here," she said. "It will take some time to realize I've actually done it but I am just very happy now."
Petkovic tore ligaments in her right knee at the 2008 Australian Open and was out for eight months.
"Rehabilitation was long and hard but made me a stronger person," the 21-year-old said. "Winning this title shows I am a better player now."
No. 66 Olaru, who upset top-seeded Alize Cornet in Saturday's semifinals, also played her first career final.
She had won both previous clay-court matches against Petkovic, but struggled throughout this time.
"I am obviously disappointed, I wanted to play better tennis today," Olaru said. "But I had a great week and must be satisfied with that."
Petkovic dominated the first part of the match with powerful groundstrokes. She raced into a 5-0 lead, failed to serve out the set at 5-1, but broke Olaru immediately afterward with a backhand winner.
The second set went with serve for the first six games. At 3-3, Olaru missed three break points and lost her own serve in the next game.
Petkovic wrapped up the victory with a service winner on her first match point.