Asinof was born in Manhattan and lived in and around New York City for much of his life. In his youth, he worked in his family's tailoring business. He graduated from Swarthmore College in 1940, then played briefly as a minor-league first baseman in the Philadelphia Phillies' organization. During World War II, Asinof served in the U.S. Army on Adak in the Aleutian Islands. He was married for five years to Jocelyn Brando, an actress who was the elder sister of Marlon Brando; the marriage ended in divorce in 1955.
Besides playing the game seriously, Asinof wrote extensively about baseball. His 1955 debut novel, Man on Spikes, was based on the experience of a friend, Mickey Rutner, who played minor league ball and twelve games in the majors. The work was chosen as one of "the golden dozen" baseball books by noted author Roger Kahn.
Asinof's most famous book, Eight Men Out, painstakingly reconstructed the events of the Black Sox scandal that marred the World Series between the Chicago White Sox and the Cincinnati Reds in the same year that Asinof was born. The book was published in 1963; the screenplay for the film Eight Men Out, co-written by Asinof and director John Sayles, appeared in 1988. An article in the September 2009 issue of Chicago Lawyer magazine argued that Eliot Asinof's 1963 book Eight Men Out, purporting to confirm Jackson's guilt, was based on inaccurate information; for example, Jackson never confessed to throwing the Series as Asinof claimed. Further, Asinof omitted key facts from publicly available documents such as the 1920 grand jury records and proceedings of Jackson's successful 1924 lawsuit against Comiskey to recover back pay for the 1920 and 1921 seasons. Asinof's use of fictional characters within a supposedly non-fiction account added further questions about the historical accuracy of the book. Asinof also worked on other projects related to the scandal, including TV documentaries such as the 2001 ESPN Sports Century Flashback: The 1919 Black Sox Scandal and the 2005 The Top 5 Reasons You Can't Blame the 1919 Chicago White Sox for "Throwing" the 1919 World Series to the Cincinnati Reds.
In 1968, Asinof signed the “Writers and Editors War Tax Protest” pledge, vowing to refuse tax payments in protest against the Vietnam War.
Asinof wrote other novels and nonfiction books unrelated to baseball including The Fox is Crazy Too (1976), the story of skyjacker Garrett Brock Trapnell. His career as a scriptwriter was curtailed when he was blacklisted for a time during the 1950s.