Ayako Okamoto of Japan converted a key birdie at the 16th hole yesterday and shot 1-under-par 71 to win the $250,000 World Championship of Women's Golf at Lake Lanier Islands, Ga., by one stroke over Betsy King.

Okamoto, suffering from a cold, earned $81,500 for the victory, a record in women's golf.

"I don't really know why I won," she said. "I had the lead in the U.S. Open and du Maurier Classic when I felt a lot better than now and couldn't hold it. I guess it shows it doesn't matter how you feel but how you play."

Okamoto led the elite 12-player field with a four-day total of 6-under-par 282. King closed with 71 for 283 and third-round coleader Jane Geddes 73 for 284.

King earned $43,500 and leads the 1987 LPGA tour with $424,175 in winnings. Geddes rallied with six birdies over the final 12 holes after seeming to fall from contention when she put two tee shots into Lake Lanier at No. 5, three-putted the hole and took quadruple-bogey 9.

King moved into a tie with Okamoto with birdies on 15 and 16. But the Japanese veteran regained the lead on her birdie at 16, a par 5.

Okamoto, with her fourth victory on the U.S. tour this year, moved into second place on the 1987 list at $411,995. Geddes picked up $28,900 but dropped from second to third at $382,830.

King finished about 20 minutes ahead of Okamoto and watched on television as Okamoto played the final hole. When the winner placed her second shot on the par-4 hole 6 feet from the pin, she said, "That's it . . . I had my chances. I missed some really makable birdie putts, especially at 13 where I slid a three-footer past the hole. But, overall, I played very well. It was just that when it counted, Ayako did what she had to do to win."

PGA Tour: John Inman sank an 18-foot birdie putt on the 18th green to cap a round of 4-under-par 66 for a 72-hole total of 265 that captured the $450,000 Provident Classic at Valleybrook in Chattanooga, Tenn. Rocco Mediate and Bill Glasson lost by one shot.

Inman, 1985 NCAA champion, posted his first PGA Tour victory and the second win by a 1987 tour rookie. After his birdie on the final hole, he waited Mediate, in the last foursome, bogeyed 18. That cost Mediate dearly. He and Glasson each won $39,600; Inman, $81,000.

Inman said he put his faith in an 11-year-old putter he has used since he was 13.

"I just said, 'John, this putter has brought you through many times.' Then, I just hit it and the ball went right in the middle {of the hole}."

Senior PGA: Miller Barber weathered a three-hole slump to hold off Bruce Crampton by a stroke in the $300,000 Showdown Classic at Jeremy Ranch, Utah.

Barber led Crampton by five shots only to lose four strokes to par on 13 through 15. And he failed to get out of a trap on 18 on his first try, but then hit close enough to assure a par 72 for a 54-hole 210 and $45,000.

U.S. Amateur: Billy Mayfair, 1987 NCAA player of the year from Arizona State, defeated Eric Rebmann, 4 and 3, in Jupiter, Fla., for the 87th championship.

Mayfair, 21, never trailed in the 36-hole final but didn't take the lead for good until the 22nd hole. He was consistent on the 6,879-yard Jupiter Hills Club course and the match ended as Rebmann, 23, a University of Tennessee graduate from Plantation, Fla., bogeyed two successive holes.

Mayfair adds this title to his 1986 U.S. Public Links laurels.