Billy Mills, a 26-year-old Marine from Coffeyville, Kan., took 46 seconds off his best time ever yesterday and gave the United States its first gold medal in the history of the Olympic 10,000-meter run.

Mills sped by Mohamed Gamoudi of Tunisia and Ron Clarke of Australia on the last lap to win in the Olympicrecord time of 28:32.2.

Gerry Lindgren, the 13-year-old who beat Mills at the U.S. Olympic trials in August, finished ninth despite an ankle sprain suffered in a workout Monday. Pyotr Bolotnikov of the USSR, defending champion in the event, finished out of the top ten.

Mills' medal was the only one for the U.S. in track today. Finland's Paul Nevala won the javelin with a throw of 271 feet, 21/4 inches. Gergley Kulcsar of Hungary was second and Jan Lusis of the USSR third.

Britain's Mary Bignal Rand jumped a world-record 22 feet, 21/2 inches to win the women's broad jump.

The U.S. took home three more gold medals in swimming. Ken Sitzberger won the 3-meter springboard dive with Harvard graduate Frank Gorman '59 second, and Larry Andreason third.

Cathy Ferguson set a world 100-meter backstroke record of 1:07.7 in beating France's Christine Caron for the gold medal. Ginny Duenkel of the U.S. war third.

Dick Roth and Roy Saari came in 1-2 in the 400-meter individual medley, with Roth setting a world record of 4:45.4 Carl Robie took fourth for the U.S.

The U.S. freestyle relay team, with two Yale undergraduates and a Yale alumnus among the four members, broke the world record with a 3:33.2. Mike Austin, Yale's captain last year. Steve Clark, now a Yale senior, and Don Schollander, a freshman, were on the team.

Schollander also broke the Olympic record in the 400-meter freestyle trials with a 4:15.3.

Middleweight wrestler Dan Brand took a bronze medal, the only other medal of the day for the U.S. team.

Bob Hayes led a full complement of three American sprinters into the 100-meter dash semifinals, and Yale graduate Jay Luck, Billy Hardin and Rex Cawley qualified in the 40-meter hurdles.

In swimming trials, American swimmers Chet Jastremski and Wayne Anderson moved into the finals of the 200-meter breaststroke. In the women's 100-meter butterfly Kathy Ellis, Donna De Varona, and Sharon Stouder broke the Olympic record in succession in the trials, with Miss Stouder posting the best time, 1:07.0.

Three Japanese, two Bulgarians, two Russians and a Turk won gold medals in freestyle wrestling, while Hans Zdralzila of Czechoslovakia won the middleweight weightlifting title. The Netherlands took the gold medal in team bicycle road racing.