Defending champion Inbee Park closed with a 72 to tie for 14th at finish at 5 under. That will be good enough when the new world ranking comes out to stay No. 1 for the 56th consecutive week since the South Korean replaced Lewis at the top.
Lewis will supplant Lydia Ko in the second spot. Ko, who didn't play in North Texas, moved to No. 2 after her win last week in San Francisco only days after her 17th birthday.
Wie had her fourth consecutive top-10 finish, including her first win in nearly four years at home in Hawaii after a runner-up finish in the season's first major.
Wie, playing five groups ahead of Lewis, was 6 under in a span of seven holes — Nos. 9-15. When she made a 4-foot birdie putt at No. 15, she was 11 under and only two strokes behind Lewis, who was finishing her only bogey of the day at the par-3 11th.
Lewis' tee shot at the 175-yard 11th half-buried in the sand just under the lip of the bunker. Lewis had sand in her face after hitting out, and couldn't save par. But she got that lost stroke right back with a long birdie putt at the par-4 12th.
While Wie was finishing with consecutive bogeys, Lewis had an incredible par-saver at the 390-yard 15th hole, where deciding against an iron she hit her drive into the water. After dropping from about 140 yards, she hit her approach to about 3 feet.
Wie's eagle at the 510-yard 10th hole was her third of the week there. But after missing the green at the 180-yard 17th for a bogey, she hooked her 8-iron approach at the closing par 5 into the trees and bogeyed.
"I thought I had it on 17, just nuked it over the green," Wie said. "I just hit a wall on the last hole, which is disappointing for me. At the same time, 4-under par on the last day, I'll take it."