Eastman was born in Los Angeles, California, into a working class family employed in motion pictures. His father worked at Warner Bros. as a grip, and his mother was a longtime secretary for Bing Crosby. Eastman's sister Carole also became a screenwriter. Eastman began his career working in the Crosby office and appears as a prominent extra in many Bing Crosby films. He was working in the script department at CBS in the 1950s and had written several plays that found a place in Los Angeles theatre, including La Peregrina, Victorey, The Root of the Iceplant and The Hamster of Happiness. The Hamster of Happiness became a screenplay produced at NBC as an Experiment in Television, with Susan Tyrrell and Mildred Dunnock, and later a motion picture at Lorimar under the title Second-Hand Hearts, directed by Hal Ashby. Eastman preferred holding onto his original screenplays for most of the early 1960s, preferring to hire out on other projects. He is widely considered one of Hollywood's most accomplished script doctors. Examples of this uncredited work include Otto Preminger's Bunny Lake Is Missing as well as The Loved One, The Cincinnati Kid, The Americanization of Emily, This Property Is Condemned, Who'll Stop the Rain, The Planet of the Apes and Heaven Can Wait.

Eastman's screenplay Little Fauss and Big Halsy was produced at Paramount and released in 1970. He shared Esquire magazine's Best Screenplay of the Year award with Bertolucci's, The Spider's Stratagem. Star Robert Redford is quoted on page 142 of James Spada's, 'Films of Robert Redford' " That was the best screenplay of any film I've ever done,in my opinion.It was without a doubt the most interesting,the funniest,the saddest,the most real and original."

Eastman wrote and directed The All American Boy for Warners starring Jon Voight.This film is an epic debut for Eastman as a director and stands as one of the masterful works of 1970s.

In "Above the Line" conversations about the movies. Lawrence Grobel's book quotes Robert Towne of Chinatown fame citing Eastman as an early influence, "Honeybear I Think I Love You, a very influental screenplay affected me strongly because there was a guy who was able to use life around him and push as far as anybody writing a novel was going to push."