Thompson's late heroics completed a round of 3-under 69 and put her at 16-under 272 -- one better than the hard-charging Lewis.
The 18-year-old notched her second victory of season and third of her LPGA Tour career.
Lewis settled for a 2-under 68 after missing a chance to force a playoff on the 18th when she missed a short birdie try.
Capturing third place at 13-under was So Yeon Ryu (69).
Inbee Park (69) took fourth at 11-under 277, followed by Pornanong Phatlum (71) and Suzann Pettersen (70) in fifth at minus-10.