After a straight sets, yet workmanlike, victory over compatriot Bethanie Mattek-Sands in her opening match, Stephens had looked poised for another uncomplicated outing as she strolled through the first set against Petkovic.
But the world number three ran into considerably more resistance in the second set as Petkovic dug in, secured a key break then held serve to level the match.
The 91st-ranked German dictated play in the third set, breaking Stephens twice, and closed out the match with her second break.
Petkovic faced three break points through the first two sets and lost each one, but in the third it was the 30-year-old German applying all the pressure while not facing a break point herself.
"I didn't serve great but that's not what lost me the match," Stephens said.
"She just played better than me."
Petkovic will next play either Swiss sixth seed Belinda Bencic or Japan's Nao Hibino.
American Jennifer Brady cruised to a 6-1 6-4 win over Russian Natalia Vikhlyantseva and will face eighth-seeded Kazakh Yulia Putintseva in the second round on Thursday.
China's Zheng Saisai defeated 19-year-old Brit Katie Swan 6-2 6-4 and Magda Linette of Poland dispatched Australian Olivia Rogowska 6-4 6-1 to set up second-round showdown with third-seeded Indian Wells champion Naomi Osaka on Thursday.
Belgian Ysaline Bonaventure fired four aces in her 6-3 6-3 win over Ukrainian Anhelina Kalinina and American Allie Kiick led Briton Katie Boulter 6-4 4-4 before their second-round match was suspended due to rain.
(Reporting by Steve Keating in Toronto, Additional reporting by Rory Carroll in Los Angeles. Editing by Peter Rutherford)
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