The Romanian admitted to feeling the pressure as the second seed at Flushing Meadows, but showed no signs of that in a 6-2 6-1 thrashing of Slovak Jana Cepelova.
Halep, 22, said she was growing in belief in New York, beginning to relax after negotiating the early rounds.
"I think I handled it very well now, because first round was tough because of the pressure, but now I feel OK," she said.
"I feel relaxed, more relaxed than first days here. I saw that even if I'm second seeded, it's like normal. It's like before.
"So I have just to enjoy the match, to enjoy the game, and just to be happy.
"I am here, and I think I deserve to be here because I won many matches, good matches with top players, and I did some great results.
"So I'm looking forward to keep this way going ahead and just to feel the ball every day and to be more confident day by day in myself."
Particularly pleasing for Halep, who faces either Croatian Mirjana Lucic-Baroni or Israel's Shahar Peer in the third round, was getting off court quickly.
Halep hit 16 winners against Cepelova to claim victory in 56 minutes on a warm day.
"Now I feel great because I finished very fast. Outside is so hot and is not easy to play. But I played my style," she said.
"I was aggressive. I started a little bit slow, but then I just wanted to make a step forward in the court and just to hit the ball and to take the ball fast. I returned her very well today.
"And also my serve helped me sometimes in the more important moments. I did a great job today, and I'm really happy with my game."