Thompson shrugged off a delay of just over an hour due to the threat of lightning to finish 17 under par, with overnight leader Ilhee Lee her nearest challenger on 14 under after a 70.
World number two Suzann Pettersen and Shanshan Feng, who won the Reignwood Classic last week with an eagle on the 72nd hole, share third place on 11 under.
"The last few events have actually been a lot better with my putting," Thompson, 18, said. "I went back to my old style of putting and just went to how I was putting when I was really little.
"So I'm feeling really confident with my putter, and mainly that is what putting is all about. It's just getting over the putter and saying you're going to make it."
Thompson trailed South Korea's Lee by one shot at the start of the day but quickly moved ahead with three birdies in an outward half of 32 and picked up further shots on the 10th and 13th.
"I think this game is all about momentum," Thompson added. "Once you make a few birdies you feel good and just try to keep that going."