Grantham began her career with a supporting role as a sister in the drama film Southern Hospitality (1971), which was filmed in Greensboro, North Carolina. She also served as the costumer for the film. The following year, she was cast as the ill-fated Phyllis Stone in Wes Craven's controversial 1972 horror film The Last House on the Left. Grantham starred alongside Sandra Peabody, David Hess, and Jeramie Rain. She was initially reluctant to join the production due to how brutal the subject matter in the screenplay was. However, she felt more comfortable about starring in the project after meeting Wes and Sean S. Cunningham. In a retrospective interview in 2012, Grantham discussed meeting Craven and Cunningham and the impact of The Last House on the Left, stating:

In 1973, she appeared in the documentary film Loops, which was directed by Shaun Costello and featured her Last House co-star Fred J. Lincoln who also appeared in the documentary.

Grantham revealed in the interview that the scene in The Last House on the Left in which her character was forced to urinate, it was not a bag containing liquid, in fact, it was Grantham who urinated herself for the sake of making the film, despite the fact that in David A. Szulkin's book on the making of the film it notes that a wet makeup sponge was concealed in her jeans. In 2002, Grantham appeared in the documentary It's Only a Movie: The Making of Last House on the Left, included in the film's 30th anniversary DVD release.