Like a lost novel by J.D. Salinger, “The Holdovers” arrives out of the mists of time. Directed by two-time Academy Award-winner Alexander Payne (“The Descendants”) and written by David Hemingson (TV’s “Black-ish”), the film is set at Barton, a fictional Catholic prep boarding school outside of Boston in 1970, where the students torment one another and the teachers, well, the teachers also torment the students. Chief among these is bearded, goggle-eyed ancient history professor Paul Hunham (Paul Giamatti of Payne’s 2004 hit “Sideways”), who wears a sweater vest and corduroy pants and jacket and hands out exam papers sporting a plethora of Ds and Fs with great relish.

When one of the many privileged and entitled students objects, pointing out that he won’t get into Cornell with this grade, Hunham offers to let them retake the test after the Christmas/New Year break when most, but not all of the students will be reunited with their families. Angus Tully (the tall, Adam Driver-ish Dominic Sessa, making a strong debut), who is miserable, angry and untrustworthy, expects to go to Saint Kitts with his mother and her new husband. When we first meet Hunham, he is muttering the word, “Philistines” while grading papers and smoking a pipe. The film’s troubled fellow protagonist Tully, for his part, argues with the jock Teddy Kountze (Brady Hepner, “The Black Phone”), whose father owns a helicopter, over stolen cigarettes and porn.

Cue the Chambers Brothers’ “Time Has Come Today.” In the facility’s vast kitchen, grieving supervisor Mary Lamb (a magnetic Da’Vine Joy Randolph), a Black woman from Roxbury whose son Curtis, a stellar Barton graduate, has recently been killed in Vietnam, reigns regally.

At a gathering of the teachers, Mary and students at the school’s church, the priest presiding over the ceremony honors Curtis in his address to the congregation. Curtis’s photo in uniform adorns a wall in front. Curtis joins the many other Barton graduates who have fallen in service since 1797 when the school was founded.

Many Barton “boys” wear their hair long in what they think is a form of “civil disobedience.” Hunham will later refer to the students as “troglodytes” and “entitled little degenerates.” When Hunham is forced by the vindictive headmaster to remain at the school to supervise the boys being “held over,” Hunham strongly objects, not that he would be anywhere else. Tully’s mother tells him over the phone that she and her new husband want to go on a “honeymoon.” Tully is not invited.

Thus, Hunham, Mary, who remains to cook, and Tully form an unlikely trinity. Like Hunham, Mary lives on campus. At night, she watches TV and drinks whiskey. Hunham joins her. These newly-befriended buddies watch “The Newlywed Game,” of course.

In the third act, Hunham drives Tully and Mary to Boston. Mary wants to visit her pregnant sister (Juanita Pearl), who lives on top of a Roxbury triple-decker. Tully and Hunham attend a Christmas Eve party hosted by the school’s secretary Lydia Crane (Carrie Preston). The school janitor Danny (Naheem Garcia) arrives. Tully kisses a girl (Darby Lee-Stack). Disparate souls coalesce; lives are shared. The cast is a delight. Tully and Hunham go to the MFA and tell each other secrets that are strictly “entre nous.” With novel-like magic, “The Holdovers” makes you fall in love with its damaged miscreants.

(“The Holdovers” contains drug use, profanity and sexually suggestive content)

“The Holdovers”

Rated R. At AMC Boston Common and suburban theaters. Grade: A-