Billie Jean King, who has won more matches than any woman in the 15-year history of the Federation Cup, and Chris Evert, a rookie in the competition, gave the United States its sixth victory today in the premier international team event of women's tennis.

King, winner of 14 straight Federation Cup singles matches and 25 of 29 in the seven years she has represented the U.S. dating back to the 1963 inaugural, defeated Dianne Fromholtz, 6-1, 6-2, in the critical opening match of America's 2-1 victory over Australia.

Evert then clinched the best-of-three final, coming back from 1-4 in the first set to defeat Australian Open champ Kerry Reid. 7-5, 6-3, on the grass center court at Devonshire Park.

Reid and Wendy Turnball salvaged one point for Australia, seven-time Cup winners, by beating Evert and Rosemary Casals, the No. 2 seeds in the Wimbledon championships beginning next week, 6-3, 6-3, in the meaningless doubles match.

This was the only match the U.S. team, probably the most formidable assemblage of talent ever in the Cup, lost in its week-long romp past Australia, Switzerland, France, South Africa and Australia.

The U.S. team split $40,000 and the Australians $20,000 out of the prize pot of $130,000 for the 32 participating teams.

The Australians played nearly as well as they did in upsetting Great Britain, 2-1, in the semi-finals Friday. The opposition today, however, was a notch better and more competitive.

King considered herself the under-dog against Fromholtz, a 20-year-old lefthander from Sydney who had been off-form until her rejuvenating victory Friday over Sue Barker. It was Fromholtz who beat King twice last October in the first two singles tournaments King had played since mid 1975, a Phoenix (second round) and Palm Springs (first round).

Those were the last two matches King played before surgery on her right knee in November, from which she is now making a determined comeback.

"I thought about that a lot," King said today. "Those losses were weighing on me. They were the ones that got me in the hospital. She cleaned me, and you never know. She's got that in her mind and she could do it again. I have never beaten her, so I felt I was the underdog."

Fromholtz saved one break point at 30-40 in the first game, but that was the only game she won in the set.

Fromholtz got he best weapon, the cross-court backhand, zinging in the second set and was consistent off the forehand as errors crept into King's game on both wings. Fromholtz broke for a 2-1 lead, King broke back to 2-3, but then Fromholtz ran out the set as the series suddenly looked competitive.

Fromholtz grittily held her serve from 3-40 in the second game of the final set, and saved two break points from 15-40 in the fourth game. She played inspired, aggressive tennis on those points, but King got the advantage back and broke on two forced forehand errors.

Perhaps the most critical point of the match came with King serving at 4-2 in the final set. Fromholtz had battled from 30-0 to 30-30, and then went for a backhand cross-court passing shot. King anticipated and devoured it with a forehand volley, served out the game and broke after one deuce for the match.