World number two Lewis was one of a number of players forced to play their third round on Sunday morning after high winds caused the suspension of play on Saturday.
She was one shot behind leader Morgan Pressel heading into the final round, but at one stage found herself three shots behind 36-hole leader Choi Na-yeon.
Lewis birdied the final two holes to finish the round on par and with an eight-under par total of 280 for the tournament, while Choi produced three bogeys in the final six holes as she recorded a one-over 73.
"It all happened so fast there at the end, you're fighting for every shot and then all of a sudden you make a couple of birdies and it's over with," Lewis said in the televised victory presentation.
Lewis, whose other major victory came at the Kraft Nabisco Championship in 2011, had to wait while Choi finished her final holes.
"Those last few holes are playing so hard and with the pressure, but obviously I did it so it was doable, so I tried to stay in the moment and be ready for a playoff if it happened," she said.
South Korea's Choi tied for second at six-under with compatriot Park Hee-young.
(Reporting by Martyn Herman and Josh Reich in London; Editing by Clare Fallon and Brian Homewood)
