"Definitely I feel lighter now," Halep said. "I feel much better that I could win a match finally in this tournament."
Romanian fourth seed Halep defeated US lucky loser Nicole Gibbs 6-3, 3-6, 6-2 at Louis Armstrong Stadium to book a second-round match Thursday against US qualifier Taylor Townsend.
Halep lost to Russian five-time Grand Slam champion Maria Sharapova in the 2017 first round and fell to Estonia's Kaia Kanepi last year.
"Well, the pressure was tricky today. Winning one match in three years, it's pretty tough," Halep said with a smile. "But it's good that I could go over that.
"I was stressed before the match, also on this court that I lost last year. Was not easy. But I'm really happy that I could manage in the end to play better than before."
Halep said she was thankful for a tough fight in her opener, thinking it better prepares her for the tests to come.
"I'm not feeling great at the beginning of the tournament, but always when I played tough matches at the beginning, then I went through the semi-finals or quarter-finals," Halep said.
"So I'm confident. I feel like my game, it's there. I'm moving well. I just need a little bit of mental confidence. Now I'm trying to get it."
Halep hopes to match the level she reached in last month's Wimbledon final, where she outplayed 23-time major champion Serena Williams to collect her second Grand Slam title after the 2018 French Open.
"The good thing is that I believe I can touch that level," Halep said. "If I keep working every day really hard, I'm able to do it again. So that's why I'm motivated. I'm still hungry of results, of titles. I'm sure that with matches and with tournaments I can get back there."
Halep says winning at Wimbledon has made her more relaxed.
"You just have to believe and go ahead. You have nothing to lose now in my position," she said. "I've done everything I wanted, extra winning Wimbledon. I'm pretty relaxed. But still I have expectations for myself. I'm trying to get better day by day."
Halep could become the world number one by winning the US Open title and could chase for the year-end number one ranking she held last year.
"If I'm healthy, I will go for it 100 percent," Halep said. "I want to finish number one. I still have chances, so I'm going to work for them. I'm confident I have actually a big chance. I will fight."