Gauff, the 12th seed and home favourite, had the crowd at Arthur Ashe Stadium firmly behind her as she wrapped up the match in 79 minutes on the back of a strong first serve.
"I'm super excited because this is my first win on Ashe. I think this is my fourth match here on this court and it's my first win," she said in her on-court interview.
The 18-year-old, who was French Open runner-up earlier this year, fired eight aces and lost only two points on her first serve.
Gauff will next play the winner of the match between Elena-Gabriela Ruse and Daria Saville.