The 20-year-old American was riddled with nerves before recovering to beat Luxembourg's Mandy Minella 4-6 6-3 7-6(5) in her opening match on Monday.
Minella burst into tears when she missed a difficult backhand volley to hand victory to the woman touted as the successor to Serena Williams at the head of American tennis.
"I got off to a really slow start, was nervous, tight, hands were shaking, couldn't find rhythm," Stephens said. "I just had to fight and battle.
"Being here at the US Open is a bit overwhelming.
"Literally everywhere you go, every single person knows who you are, as opposed to when you're at the French Open or when you're at Wimbledon. It's 'okay ...you're a tennis player. That's great'. Here, every person knows who you are."
Stephens was aggressive and erratic from start to finish, spraying 55 unforced errors and 38 winners.
"That's not good," she said. "I never want to have that. That many (errors), that's horrible.
"But I think I was just so nervous. I was so tight, and I couldn't really get a grip.
"I managed to play some good points and get loose. That's what helped me the most.
Minella was on track for an upset victory when she led 4-2 in the third set before Stephens broke serve and eventually prevailed in two hours and 48 minutes.
Her next task, she said, would to embrace the pressure.
"It comes with the package," said the 15th seed.
"It's exciting to play at a home slam. It's exciting to be on the court and competing.
"I think I have to take advantage of the opportunity given to me.
"Normally I'm okay. But I just think here, more expectations being seeded, as opposed to last year when I was not seeded.
"I was 40 in the world, whatever I was ranked. Now there's more eyes on me.
"I just need to play my game, hit out, not be afraid to swing the racquet.
"Just play my game and be relaxed and not have to be like, 'Oh my God, I'm holding the racquet and my hand's shaking.' I just want to be able to swing out, swing free."
Stephens is yet to join Williams in winning a major championship, but her post-match press conferences can be similarly entertaining.
"Today someone yelled to me, 'If you don't get it together, this lady is going to take your second-round prize money,'" Stephens said when asked to reveal the best advice she had received on a tennis court.
"I thought that was a good one, in a moment that's so serious."
Asked by a reporter if the match had been "hairy", she replied: "Hairy? I never heard that term before. What does hairy mean?"
That the match was complicated was the reply.
"Yes," she grinned. "It was hairy."
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- Mandy Minella
- Serena Williams