Lewis stumbled to a bogey on the 15th hole but compensated with a birdie on 16th and parred the final two holes to finish one shot ahead of Thompson at 17-under-par 271.
Lewis corralled her second LPGA Tour victory.
Thompson, who was in position to win the Mobile event last year but faltered on the final day, fired a 7-under 65 but still came up a bit short at minus-16.
Karine Icher's final-round 68 enabled her to take third at 15-under 273.
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