The 20-year-old American worked through some tight moments early on to polish off the victory in 66 minutes on Arthur Ashe Stadium, where she captured her first Grand Slam title last year.

She was breezing through the second set when France’s Gracheva, ranked 66th in the world, mustered a pair of break points in the final game.

Gauff saved both with aces as she booked a second-round meeting with Tatjana Maria of Germany, a 6-2, 6-3 winner over Argentina’s Solana Sierra.

“I served well,” Gauff said. “Can’t ask for a better start into this tournament, so hoping to continue to get better as the week, two weeks go by.”

Gauff’s build-up to the final Grand Slam of the season has been less than ideal. She fell in the third round at Toronto and lost her first match as the defending champion in Cincinnati.

But she said taking the long view was helping her stay steady as she tries for the first time to defend a major title.

“The last couple of weeks were tough, and I was, like, ‘I have to do this and do that.’

“But I don’t have to prove anything to anyone except myself,” she said.

“Just learning and just realizing that I have a lot left to give this game, and whether that’s going to happen this year or in the future, I have many more years coming back here,” she said. “And I’m not going to win every year.”

She said that perspective, “and just having the belief that I can but not the expectation that I should” win had tamped down the pressure.

So did the confidence in her game that had built practice, despite her disappointing recent results.

“I wasn’t surprised about my level because I was practicing really well this week,” she said.

“It was a really good practice week. So honestly, I was just telling myself that I’m ready, I had a great practice week, I feel like I’m finding my game, whereas the other two tournaments that I played at, even the practice sessions I was doing, I just felt off.

“I knew based off how I was practicing I can find my game regardless of the scoreline. Then it’s just about executing.”