America's first test-tube baby was born in Norfolk yesterday, 3 1/2 years after two British scientists showed the world how to start the miracle of human conception in a laboratory dish.

Five-pound, l2-ounce Elizabeth Jordan Carr was delivered at Norfolk General Hospital at 7:46 a.m. by Caesarean section.

She is the first successful product of a 21-month-old "in vitro fertilization" program--that literally fertilizes human eggs in plastic dishes--at the Eastern Virginia Medical School.

Both the baby and her mother, Judith Carr, a 28-year-old Westminster, Mass., schoolteacher, later were pronounced "perfectly healthy." The baby had her first feeding and, doctors said, took an ounce of formula "very well."

"The baby cried right away and that was very reassuring," said Dr. Mason Andrews, who performed the Caesarean. "It was a relief to know this was a normal baby."

"I think this day is a day of hope," said Dr. Howard Jones, another doctor involved in the project who said the technique offers the possibility of childbirth to approximately 600,000 American women who are unable to have children because of damaged or missing Fallopian tubes. Those are the passages by which a fertilized egg normally reaches the womb--and without which normal conception is impossible.

Carr and her husband, mechanical engineer Roger Carr, were among those affected. Complications during unsuccessful pregnancies had forced removal of her tubes.

A team of doctors and scientists headed by Drs. Howard and Georgeanna Jones, husband and wife, came to the Carrs' aid last April, successfully joining Roger Carr's sperm in a laboratory dish with a ripe egg cell the doctors had removed from her ovaries. They transplanted the resulting "conceptus," a growing clump of new cells, into her womb to let the gestation process take its normal course.

The Norfolk birth comes as doctors in three countries rapidly are making this a regular, rather than a strange, event. At least 63 more women in three countries are now pregnant by this method.

A woman's chance of having a child in this way--about one in 10 according to recent reports from centers abroad--is beginning to approach one in five, Howard Jones said yesterday. Five more Norfolk patients are expecting children as a result of increasing successes in the last four months.

At least 48 women are carrying babies conceived with the laboratory aid of Drs. Patrick Steptoe and Robert Edwards in Bourn, England. The world's first test-tube infant, baby Louise Brown, was delivered on July 25, 1978, by their efforts, and they have seen at least seven more successful births since.

Nine Australian women are pregnant through the laboratory efforts of a group of doctors at the Queen Victoria Medical Center in Melbourne. The doctors have successfully delivered at least nine such babies.

There are new efforts at the University of Southern California Medical Center, where there is one pregnancy, and at the University of Texas Health Science Center in Houston. Yale doctors have said they expect to start an effort of their own.

What the Norfolk birth shows, said Andrews, "is that medical science is pushing forward all over the world." The 62-year-old physician, who is Norfolk's vice mayor, is one of the doctors who have pushed the project forward despite opposition from some church groups.

Andrews, who helped organize the private medical school eight years ago and is its chief of obstetrics and gynecology, said in an interview last week that so many couples are desperate to have children, it seems "almost immoral" not to help them.

Still, critics complained yesterday that the Virginia doctors were treading on dangerous ground. The Rev. Jerry Falwell, head of the conservative Moral Majority, said that the scientists are "delving into an area that is far too sacred for human beings to be involved in."

Success did not come quickly to the Norfolk group. In 1980 the group made 30 attempts at laboratory fertilization with zero results. This year, combining Melbourne, British and some new Norfolk methods, there have been the six pregnancies so far in some 50 tries. Four of the six have been achieved since September.

The process includes the use of fertility-inducing hormones by Dr. Georgeanna Jones, a gynecological endocrinologist. This makes the would-be mother ovulate--produce an egg--at a fixed time.

There is exact monitoring of the would-be mother's hormonal status by Dr. George Wright, another member of the team. He tells Howard Jones when to remove the ripening egg from the mother.

Dr. Edward Wortham, reproductive biologist, places the harvested egg in a careful mix of chemicals and nutrients, including--just one detail--water that is "super-purified," then twice distilled to eliminate all pollutants. Wortham and co-workers then join egg and sperm in a shallow plastic dish to give them their chance to join and start conception.

"All this sounds so simple," Wortham says. "But there's a lot of stress in it all. And it works because a lot of people have worked a lot of long hours to make it go."

Few have proved as indispensable to the Norfolk effort as have the Doctors Jones. He is 70, she is 68. They came to Norfolk after retiring from Johns Hopkins University in Baltimore. As he puts it, "We thought it was an alternative to fading away."