Three strokes ahead of playing partner Amanda Doherty and four ahead of Ryu entering Sunday's (Monday AEST) round in Cincinnati, Woad closed with a one-under 69 for a two-stroke victory. The 22-year-old finished at 12-under 268.
"I generally played pretty well," Woad said.
"I just played pretty good tee-to-green. I hit a lot of greens, hit a lot of fairways. And it's pretty windy out there, so I think that was the key, obviously, to having the lead."
World No.1 Nelly Korda, who began the day nine strokes back after a third-round 72, shot a 67 to tie for eighth at five under after winning in her previous two starts.
Woad won for the second time on the LPGA Tour, following a victory last year in the Women's Scottish Open in her professional debut.
"This one is definitely, I think, is a little sweeter than the first one because I wasn't really expecting that," Woad said.
"This one, I've seen how good everyone is out there, so it's good to win again."
She made a 20-foot birdie putt on the par-4 17th to open a two-stroke lead, with Ryu (67) parring the par-3 18th soon after in the group ahead to post at 10 under.
Woad overcame a double bogey on the par-4 sixth. The former Florida State star birdied the seventh, parred the next five and dropped a stroke on the par-4 13th. After three more pars, she got the long birdie try to curl in on 17.
"Not an easy putt from where I was above the hole with a lot of break, and had a little pace going in, so pretty glad I hit the hole," Woad added.
"Gave me a two-shot cushion on a par 3, so pretty happy with that."
Miyu Yamashita (64) was third at nine under, Ruoning Yin (66) was eight under, while Doherty (71) and Jin Young Ko (65) were seven under.
Australia's Robyn Choi charged home with a 65 to tie for eighth at five under, while countrywoman Cassie Porter (69) was tied 30th at one under.
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