Lang birdied the par-5 18th hole three times in succession to hold off Seo Hee-Kyung, Park In-Bee and Chella Choi and secure victory.
Lang missed her two-foot birdie attempt on the hole in regulation instead settling for the play-off after Seo and Park, playing with Lang in the final trio, could also only manage par on the final hole.
"I gathered myself (after missing the putt on the 18th) and it was really good experience to have that playoff go on," said the 26-year-old Texan.
"I can't believe it took me seven years to win a tournament out here. I hadn't been that good under pressure and I'm getting better. I'm so thankful it happened this week."
Choi was eliminated on the first extra hole, while Park dropped out on the second before Lang finally saw off Seo on the third.
"I got better with each putt, because I had to make two other putts to stay in the playoff," said Lang. "The last putt to win, I felt way better than I did in regulation."
Seo, who lead after 11 holes, had chances to win the tournament on both of the first two play-offs holes but could sink neither of her less-than-15-feet putts.
“I tried my best,” Seo said. “I made good shots up there but the hole was in a really tough position. I just didn’t get good breaks.”