Though she was briefly caught at the top by a red-hot Piller with eight holes to play, Thompson picked up two more shots over the closing stretch, along with a bogey on 17, to post an 18-under-par total of 266.
American Piller, bidding for her first win on the LPGA Tour, closed with an eight-birdie 64 to tie for second with Salas (70).
The 20-year-old Thompson, who will climb from 13th to sixth when the new world rankings are issued on Monday, earned a winner’s cheque of $300,000 for her first LPGA victory of the season.
“It feels amazing,” Thompson said after tapping in a two-footer to par the last. “It still hasn’t really hit me yet because everything happened so fast.
“I was just trying to focus on my own game … having fun in between shots and I think that’s what helped me shoot six under today.
“It’s definitely momentum going into the next week being a major,” said Thompson, who left the course after her post-round interviews for Detroit Metro Airport to board a plane for Scotland and next week’s Women’s British Open at Turnberry.
Thompson, who won her first major title at last year’s Kraft Nabisco Championship, made a sizzling start to the final round with birdies at the first, fourth and fifth to cut Salas’ overnight lead to just one shot.
When Salas bogeyed the par-four seventh, she dropped back into a three-way tie at the top with Thompson and Piller, who had reeled off five birdies in the first eight holes.
Salas’ challenge effectively ended with another bogey at the 10th and Thompson took control of the tournament with further birdies at the 10th, 11th and 15th.
South Korea’s Ryu So-yeon (66) and American Kris Tamulis (68) finished joint fourth at 15-under while Korean world number one Park In-bee tumbled back into a tie for 44th after closing with a 76.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine)