The 22-year-old Lee shot a 5-under-par 67 in the final round. Webb had 70 after sinking a 20-foot putt on the last hole to tie Lee at 14-under 274, setting up the playoff.
Lee parred the first playoff hole and won when Webb, a Hall of Famer, missed a 4-footer for par.
The young Korean had trailed leader Sophie Gustafson by nine shots entering the final day's play.
Song-Hee Kim was third at 13-under 275. Gustafson, who slipped to a 7-over-par 79 in the final round, tied for fourth with Jane Park at 277.
"I didn't expect to win," Lee said.
The victory was her third on the LPGA Tour.
Annika Sorenstam, the tournament host, shot a 71 in the last round and ended in a tie for 32nd place at 4-under 278.