The Swiss was occasionally bamboozled by the Czech veteran's serve-and-volley game but kept his composure to triumph on Hisense Arena.
The pair exchanged breaks, and a plethora of line-call challenges, in a thoroughly entertaining third set before Stepanek went long to send Wawrinka into the third round for the eighth year in a row.
"Really happy," the 30-year-old said. "It was a good match in general. Three sets win against Stepanek."
Stepanek was hoping to become the oldest player to reach the third round of a grand slam since Jimmy Connors in 1991 and unlocked his full bag of tricks in the attempt.
French Open champion Wawrinka has never been a slouch around the court, however, and enjoyed clear superiority when he was able to dictate points from the baseline.
Wawrinka will next meet another Czech, Lukas Rosol, in the half of the draw left weakened by the first round exit of Rafa Nadal.
Wawrinka's first round match against Dmitry Tursunov lasted only two sets before the 33-year-old Russian retired hurt but he declared himself happy with how the tournament was going for him.
"So far it's been okay," he added. "Two matches, two victories.
"Today was a really good level on the tennis side.
"Just focus on every match, trying to rest between, trying to be ready for the next one."
(Reporting by Nick Mulvenney Editing by Alison Williams and Justin Palmer)
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