Navarro, seeded 13th, had never previously advanced past the first round at Flushing Meadows but her stunning win over compatriot Gauff has landed her a spot in the quarter-finals against Spain's Paula Badosa.
"I've been out on big courts before where I just felt totally overwhelmed and almost like it's an out-of-body experience, but I didn't feel like that today," Wimbledon quarter-finalist Navarro told reporters.
"I felt comfortable from the time I stepped out onto the court, which I was a little bit surprised about. I kind of had prepared myself for the worst just in terms of feeling overwhelmed and nervous.
"It's a pretty crazy court. The energy in New York is unmatched, just really (an) amazing experience."
While Gauff served poorly and made several errors, Navarro's aggressive style and superior court coverage often put the champion on the back foot.
Navarro, who constantly attacked Gauff's second serve, said she is making a conscious effort to play proactively against the top players - a strategy that has helped her rise up to a career-high number 12 in the world.
"I think I'm totally different, definitely, as a player. I play more aggressive, every part of my game has improved. Also I just play with more confidence and more belief," Navarro said, adding that she now makes better decisions on court.
"Partially because the players I'm playing against, they'll shut it down if I don't make that more confident, aggressive choice. Also just because I think I have more belief in myself to be able to actually execute those types of shots.
"I think I believe that I can play tennis with the best players in the world. I deserve to be on this stage, I belong in these rounds of Grand Slams and I can make deep runs."