In 1956 Schenectady, New York, waitress Shirley Roque marries auto mechanic Jack Muldowney over the mild objections of her singer father Tex, who wants her to be self-sufficient rather than having to rely on a husband. Jack buys a gas station, Shirley becomes a housewife, and they have a son.

For fun, Jack races his hot rod against others on deserted stretches of road late at night. One time, Shirley talks him into letting her drive. She wins and continues winning. A chance encounter with professional driver "Big Daddy" Don Garlits inspires her to look for sponsorship from one of the major car manufacturers, despite her husband's skepticism. As this is the late 1950s, a pretty housewife is not taken seriously, especially since there are no women professional drivers, but when she returns home, Jack tells her that he can build her a dragster.