World number two Lewis, who went into the final round seven strokes behind overnight leader Korean Bo-mee Lee, finished at 11-under 205 following crucial birdies on all last three holes.
Lewis levelled with Lee following two extraordinary putts from 25 feet and 12 feet on the 16th and 17th holes respectively. She took the lead with another 25-foot putt on the last hole, and consolidated victory when Lee's last putt went long.
The win marks her fourth LPGA Tour title of 2012 and her third successive top-six finish at this tournament.
"It was pretty unexpected to make those last three birdies. They were all pretty long putts so it wasn't easy,” Lewis said.
"I knew I was a ways back," Lewis said. "I thought if I got to 10 under, it would be close. To shoot a 64 on the final day is always good."
Three bogeys and three birdies gave Lee enough for an even-par 72 and a second-place finish, who started the final round with a four-stroke lead. Japan’s Ayako Uehara took third place with a nine-under 207.
Defending champion Momoko Ueda of Japan shot a 73 to finish tied for 27th.