"They told my husband that he would have an hour with her and then he would die, but that time turned into two, and these two, one day, and then a week," her mother said in a video posted by the hospital.
He was tall, weighing 2.26 kg and 40 cm, in good health, according to a hospital statement.
Saybie became the smallest newborn in the world to survive childbirth, according to the University of Iowa registry.
His birth weight, which equaled that of a large apple, was 7 grams smaller than that of the baby who had held the record, born in Germany.
"Every life is a miracle, but those who challenge the possibilities are even more so," Edward Bell, a pediatrician with the record, told AFP.
"I feel blessed," said the mother. "It's the smallest baby in the world and it's mine!"