Williams, who received medical attention from a trainer late in the first set, saved her best tennis for the biggest moments, breaking Petkovic for a sixth time in the final game to make up for a dismal second set.
Asked in an on-court interview to describe the encounter, the 38-year-old former world number one was almost at a loss for words.
"I don't know honestly. I'm still trying to figure it out," she said to laughs from the crowd on a sunny and windy day in the California desert.
"Every day is not your best day but that doesn't mean the heart and desire aren't there."
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Thursday's match was just Williams' seventh of the year and first since January's Australian Open, where she fell to Simona Halep in the round of 32.
The win sets up a mouthwatering second-round clash with third seed Petra Kvitova, who holds a 4-2 edge in their previous meetings.
Canadian Eugenie Bouchard also required medical attention during the second set of her closely-fought evening match against Kirsten Flipkens, where she fell 7-5 3-6 7-5 to the German.
It was unclear what the problem was with Bouchard, who held a towel to her face while trainers attended to her during a medical timeout. But she appeared fine after the break.
The marathon battle included fantastic points from both players but Flipkens was ultimately the sharper of the pair, smacking a forehand winner cross court on matchpoint to advance to the second round of the tournament for a fifth time.
In other first-round winners on Thursday included Estonian Kaia Kanepi, Japan's Misaki Doi, American Madison Brengle and Russian Ekaterina Alexandrova.
(Reporting by Rory Carroll, editing by Nick Mulvenney and Sudipto Ganguly)
