Unless you were a jazz aficionado attending shows on the New York club circuit in the 1960s, it’s likely that you haven’t heard of Don Shirley. The capsule version of his musical life is that he was a prodigy, a brilliant pianist who had classical ambitions, but there wasn’t much room for black classical pianists during that era, and though he did make some appearances with symphonies, the only regular work he could find was in the jazz and popular categories. He made recordings for Cadence, and he had regular club dates, but it wasn’t the career he longed for, and he was sort of lost in the mix.

“Green Book” tells a segment of his story, with plenty of dramatic license. But it’s just as much the story of Tony Vallelonga AKA Tony Lip who, long after the events in the film, went on to become an actor, landing parts in, among other productions, “Goodfellas” and “The Sopranos” (he played Carmine).

Shirley and Vallelonga died about five years ago, both in their 80s, close friends for 50 years. The film tells of their meeting, in 1962, each about as far from the other on the personality spectrum as can be imagined, and the unlikely events that taught them the life lessons that brought them together.

Tony Lip (Viggo Mortensen) was a bouncer at the Copacabana, a big, lumbering palooka who was a good dad and husband, but had a short fuse, a vicious temper and a casual racist streak. In need of temporary work when the club was closing for renovations, he got a phone call from a friend about “some doctor” who was looking for a driver. The “doctor” was Don Shirley, living in a classy apartment above Carnegie Hall, preparing to embark on an eight-week jazz trio tour of the Deep South and knowing, through connections, that Tony was a good guy to have on your side, especially if you were a black man in the early ’60s traveling through the South.

That’s the whole set-up of this offbeat buddy movie-road movie. Tony, the lug, takes the gig working for “Doc” Shirley, the sophisticate. They hop in the big Cadillac provided by Shirley’s record company, with the two other trio members in a second car, and head due south. Tony’s main responsibility was to get Doc from one show to the next, whether it’s in a concert hall (with an all-white audience) or a private home (with only white guests).

So, there’s crude, freewheeling Tony at the wheel, babbling up a storm about whatever pops into his head, and polite, even-keeled Doc in the back, wondering what he’s gotten himself into. But Doc always makes it known that he’s running the show, and he’s a quietly demanding boss. “Make sure it’s always a Steinway (piano),” he instructs Tony. “Make sure there’s a bottle of Cutty Sark in my room every night. Ten and two on the wheel. Put out that cigarette, please.”

You know there’s going to be tension between the finicky passenger and the temperamental driver, but there’s also, due to a sentimental script co-written by Tony’s son Nick, some well-placed humor and a low-key sweetness permeating the film. It’s only a matter of time before the two guys, despite their differences, start opening up to each other, and both Mortensen and Ali have their A-games on as far as developing and delivering their characters. Yet, as the duo makes their way through Georgia, Louisiana, and Mississippi, where the racism is blatant, and the Green Book — something akin to a AAA guide book for black travelers in the South — becomes a necessity, the tensions rise accordingly.

Still, even though that frightening atmosphere lingers around them, the film sticks with its main purpose: Showing how Tony is becoming more civilized and Doc is becoming more civil. It finally turns to the big question of whether or not Tony will get back to New York in time to be with his family for Christmas. That won’t be given away here, but I think you know the answer.

— Ed Symkus writes about movies for More Content Now. He can be reached at esymkus@rcn.com.

“Green Book”

Written by Nick Vallelonga, Brian Hayes Curry, and Peter Farrelly; directed by Peter Farrelly

With Viggo Mortensen, Mahershala Ali

Rated PG-13