Amy Alcott, wearing a water-soaked bandanna around her neck to offset the 100-degree heat, shot one-over-par 72 today to win her first U.S. Women's Open golf championship with a record-setting 72-hole total.

The composed 24-year-old, who prides herself on her consistency, won by nine strokes.She birdied three holes and bogeyed four, including the 18th, to finish with 280 and earn $20,047. She received an extra $25,000 from Golf magazine for breaking the 72-hole Open record set last year by Jerilyn Britz.

Leading since the tournament began, Alcott never faltered.

She kept her cool while the heat sent scores soaring on the Richland Country Club course. Jo Ann Prentice quit after nine holes because of heat exhaustion.

The only other golfer who came close to matching Alcott during the final round was her playing partner, Hollis Stacy. Stacy carded 73 today for a four-day total of 289, good for second place.

Third was Kathy McMullen at 73 -- 291.

Nancy Lopez Melton went into the final round at 217 but had problems with the heat. She bogeyed six straight holes on the front nine and had a bogey and double bogey on the back nine for a disappointing 10-over.

Alcott surged to the top of the Ladies's PGA money-winning list, replacing Donna Caponi Young. Young tied Judy Clark for fourth here with 292.

Beth Daniel, who started the day nine strokes behind Alcott, had a catastrophic final round, suffering six bogeys and a double bogey for a 78.

Prentice began the final round at 227 and was eight over after nine holes, then withdrew from the tournament on the advice of a doctor. She was taken to St. Thomas Hospital emergency room, treated for heat exhaustion and released.

In mastering the 6,229-yard course, Alcott brought her 1980 earnings to $152,304, not counting the bonus.

Alcott, the 1975 LPGA rookie of the year, shared the first-day lead, then pulled away. Her 54-hole total of 208 was two strokes better than Young's record of 210 set in 1970 while on the way to her second U.S. Women's Open title.

In the final round, Alcott birdied hole No. 1, then drew bogeys on Nos. 2 and 4 to shoot a 37 on the front nine. She birdied the par-3, 181-yard hole No. 12 after coming inches away from an ace.

Stacy earned $11,347 for her second-place finish, McMullen $8,547 for third.

Barbara Moxness, who shared the first day's lead with Alcott, posted 299.

Sandra Post, tied with Lopez at four-over-par 217 going into today's final round, also had trouble, drawing two bogeys and two double bogeys on the front nine for a sky-high 43.

Lopez-Melton finished the tournament with a 294, 14 shots off the pace, while Post closed at 300.

Only two amateurs -- a record low number -- remained in the 60-player field after the 36-hole cutoff based on scores of 153 or lower. The low amateur, Judith Oliver of Sewickley, Pa., with a 306, received a gold pin. Lida Kinnicutt of Bloomfield, Conn., who carded a 72-hole total of 309, got a silver pin.

Alcott, a resident of Santa Monica, will be after her third straight victory as the LPGA tour moves to the Greater Baltimore Golf Classic at the Pine Ridge course this week. She won last week at Noblesville, Ind., and now boasts 12 career victories as a professional.

Alcott and Stacy were rivals for supremacy in major junior events at the outset of their careers a few years back. Winner of the USGA Junior Girls title at 17, in 1973. Alcott won her first pro tournament in 1975, the Orange Blossom Classic.