Tardy was in a three-way tie for the lead after Saturday's third round at 12-under par with Lydia Ko of New Zealand and fellow American Sarah Schmelzel.
An eagle-three at the eighth ignited her round and six further birdies against a lone bogey saw her stretch away from an elite field in the $2.2 million (£1.7m) event.
Tardy was in tears after finishing at 19-under par for the week.
"Yeah, I mean, a lot of emotions right now," she said.
"A lot of hard work and just a lot of doubt that was in my head that I could be at this level and win.
"This is special."
Tardy, who was a rookie last year, became the third player to earn their first LPGA Tour victory at Blue Bay on Hainan Island, joining Lee-Anne Pace (2014) and Gaby Lopez (2018).
Ko had three bogeys on her front nine and finished with a 71 for a share of fourth place.
Tardy admitted she had been nervous playing with one of women's golf's most famous figures.
"You know I played with her yesterday and I was very intimidated playing with her," said Tardy of the former world number one and double major winner Ko.
"I think I handled myself really well, and, yeah, it was like playing with a friend today almost.
"She made me feel really comfortable and confident out there."
Schmelzel finished second on 15-under after a final round of 69, one stroke ahead of Japan's Ayaka Furue who had a bogey-free 65 to finish.
Top-ranked Lilia Vu of America withdrew injured before the second round at Blue Bay, opening the door for France's Celine Boutier to become world number one.
Third-ranked Boutier needed to finish solo third or better on Sunday at the Jian Lake Blue Bay course on Hainan Island but a final round 68 gave her only a share of 12th on eight-under.
Boutier, 30, who won her first major last season at the Evian Championship in her native France, was second last week at the HSBC Women's World Championship in Singapore, a shot behind winner Hannah Green of Australia
