He was born in Soria, Spain, the son of Juan de Saravia and María Mayor de Vera y Morales. In 1538 he completed his studies at the College of Bologna. He entered the royal service as oidor (judge) in Naples. In 1547 he was named to the Audiencia of Granada. In 1549 he was transferred to America in order to found the Audiencia of New Granada. Later he was transferred to Lima, where Pedro de La Gasca had reinstalled the Audiencia in 1549. As president of the Audiencia in Lima he occupied the position of interim Viceroy of Peru from July 1552 to July 1556.
During this time, the Audiencia had to combat the major rebellion of Francisco Hernández Girón. Bravo de Saravia is seen as being one of the major contributors to the eventual defeat and punishment of the rebels, due to his great activity and service during that time.