Born in Cleveland, Prescott graduated from Williams College in 1930. He began his career as a researcher for Newsweek, then known as News-Week, and became the literary editor of Cue Magazine before joining the Times, where he wrote three or four book reviews every week from 1942 through 1966. His reviews showed a preference for traditional novels with strong narratives and clear characterizations. In 1958 he reviewed Lolita by Vladimir Nabokov and described it as "dull, dull, dull in a pretentious, florid and archly fatuous fashion." In 1961, Gore Vidal wrote a scathing portrait of Prescott as a reviewer. Vidal later wrote that Prescott was so offended by his depiction of a homosexual love affair in The City and the Pillar that he refused to review his work or allow the Times to review it. (Reviews of Gore's books continued to appear in the pages of the Times after 1948, when The City and the Pillar was reviewed.) More than any other reviewer, he influenced sales of books across the country, and was held in high esteem.
Prescott edited three anthologies about history and after his retirement wrote two books about the Italian Renaissance.