The victory made the 19-year-old the first LPGA player in five years to win twice in her rookie season.
Overnight leader Thitikul shot a closing three-under 68 while American Kang roared home with a 64 as they finished the 54 holes of regulation at the Pinnacle Country Club tied at 17-under.
“I didn’t see a leaderboard until 18,” Thitikul said. “I thought a par would be good enough.”
The two matched pars on hole No.15, the first sudden-death hole, and then Thitikul made a birdie putt on No.16 to win.
Chella Choi of South Korea finished third, a shot behind the leaders.
Australian youngsters Steph Kyriacou (68) and Karis Davidson (71) tied for 39th at seven-under.
Thitikul had won the JTBC Classic earlier in the season, also in a play-off.
“On the second hole play-off, I had a chance to make a birdie, because it was not that far….