Alice Miller withstood 100-degree temperatures and a fast-charging Jan Stephenson today with a final-round, five-under-par 67 to capture the $400,000 Nabisco Dinah Shore tournament, the richest event on the LPGA tour and the first major tournament of the year.

Miller's 13-under-par 275 on the Mission Hills Country Club course equaled the tournament record set in 1980 by Donna Caponi.

"I tried to keep the possibility of winning off my mind," Miller said.

"I tried not to think that it was the Dinah Shore, a major tournament, on TV, and worth a lot of money.

"I sort of brainwashed myself."

Miller, 28, led by as many as five strokes early in the round but was nearly overhauled by Stephenson, who finished with a 66, the low round of the tournament. Stephenson wound up with a four-round total of 278, three shots back.

Stephenson, who has apparently rediscovered her putting touch after two years of frustration on the greens, said, "I really thought a 66 would do it, but Alice just kept coming right back."

"Jan had a real hot hand putting, but so did I," said Miller. "I just wanted to stick with my game plan; hit greens and wait for putts to go in.

"Fortunately, Jan was far enough back when we started the round, her 66 wouldn't do it."

Miller's lead dwindled to one stroke when she bogeyed the 13th hole and slipped to 10 under, but she came right back with a birdie on the 14th hole. She then sealed the victory with her sixth birdie of the day, a 12-foot putt on No. 16, and a minute later Stephenson had her only bogey of the day on the 17th hole.

"I felt I wasn't going to give her the tournament, that I really wanted to make a big charge," said Stephenson. "I did that, and I'm happy about it. Sometimes when I can't win on the final holes I lose interest and fall way out. I didn't do that today.

"Finishing second was real important to me."

Miller's strong finish gave her the $55,000 first prize. Stephenson finished alone in second place at 278 and earned $33,000.

In third place was Judy Clark, who shot a 70 and finished at 279. Denise Strebig (69) and Beth Solomon (68) were tied for fourth and veteran Pat Bradley (70) was alone in sixth place. Patty Sheehan (75), Jane Geddes (71) and Myra Blackwelder (68) were tied for seventh place.

Miller, one of the most consistent players on the LPGA Tour, had finished second, third, fourth and fifth in tournaments earlier this year. She was 11th on the money list in 1984 and today's victory boosted her 1985 earnings to $131,625, tops on the list this year.

She began the final round at eight under with a one-stroke lead over Clark and Sheehan, but made birdie putts on the third, sixth and seventh holes to jump to 11 under and put five shots between her and her closest rival.

But a bogey on the par-3 eighth hole dropped her back to 10 under, and Stephenson, who had started four shots out of first place, pulled into contention by dropping a birdie putt on the ninth hole and made the turn at seven under for the tournament.

Miller birdied No. 12 but bogeyed No. 13, and when Stephenson carded back-to-back birdies on Nos. 12 and 13, she was within a stroke of the lead.

Miller birdied the par-3 14th hole and Stephenson birdied No. 16, but Miller then made a 15-foot birdie putt on the 16th hole to go to 12 under and Stephenson bogeyed No. 17 to slip to nine under. She capped her round with a birdie on No. 18, but it wasn't enough to overtake Miller.

Defending champion Juli Inkster finished with a 69 but ended up at 288. A repeat victory would have earned her a $1 million sponsor's bonus.