After coming from behind in the first set, the Lausanne native finally prevailed 7-6, 6-3, 6-2 to move into the second round.
Wawrinka, ranked 10th in the world, just three places behind fellow countryman Roger Federer, admitted to being nervous and “very hesitant in my game”.
But the 28-year-old said this had become a habit for him in Grand Slam tournaments.
To complicate matters, Wednesday’s game was delayed by a lightning storm and rain at Flushing Meadows.
Wawrinka next faces Ivo Karlovic, a six foot ten-inch Croat who is turning to play after illness.
“He just won a tournament in Bogota,” commented Wawrinka.
“He will be very confident.”
But Wawrinka said he is also ready after getting past Stepanek.
One thing making a difference for the Swiss player, who won the Portugal Open this year, is a new coach.
Former world number two player Magnus Norman is helping boost his confidence, he said.
“We started working together exactly after the Monte Carlo Masters, Wawrinka is quoted as saying by The New York Times.
“I really believe that Magnus is going to make a big difference for me in the next few years,” he said.
“He’s helping me have the confidence to believe in my game.”