If you can imagine a mash-up of “Driving Miss Daisy” with “The Defiant Ones,” you’ll have some idea of what “Green Book” is like. The combination might sound ridiculous, but in the end Peter Farrelly’s movie works as an engagingly old-fashioned, feel-good crowd-pleaser.

The odd couple in this case is Don Shirley (Mahershala Ali), the ultra-elegant, supremely accomplished pianist who headed the jazz trio named after him, and Tony Vallelonga (Viggo Mortensen, quite a few pounds heavier than usual), the Italian lug he hires as his chauffeur/bodyguard for a tour of the Deep South in 1962 while the Copacabana bouncer is laid off during the club’s renovation.

The script, by Nick Vallelonga, Farrelly and Brian Currie, shows how the two bonded as they drove through the still-segregated region in a bright turquoise Cadillac (the two other members of the trio, cellist Dimiter D. Marinov and bassist Mike Hatton, are in a separate car), encountering a stream of bigots along the way even as the polite upper-crust shows its supposedly progressive attitude by applauding Shirley’s recitals though he’s expected to use broom closets as dressing rooms and outhouses instead of bathrooms.

Tony, who’s initially reluctant to take the job and is a bit put off by Shirley’s airs, comes to recognize his employer’s extraordinary talent and sympathize with the treatment he receives from racists of every variety. He steps in to defend his boss from threats or talk their way out of jams (it’s not for nothing that his nickname among family and friends is “Lip”).

And he introduces Shirley to pop music icons—black ones—the pianist doesn’t even know about, as well as to fried chicken (made with the Colonel’s secret recipe in Kentucky, no less).

Shirley, meanwhile, grudgingly accepts his instruction in such matters, while helping Tony to write letters to his wife (Linda Cardinelli) back home that sound less like laundry lists; they make her swoon and female friends and relatives envious. But he’s a stickler on some matters, and prods Tony to toe the line when matters of principle are concerned—as when Vallelonga’s impetuous attack on a racist cop forces the pianist to make a call to a person of influence he’d rather not bother with such things.

There are a few episodes that touch on edgier matters without going very deeply into them—as when Tony intervenes in an incident that might have been very embarrassing, given the era’s sexual as well as racial prejudices.

But it’s a sign of the movie’s basically genial attitude that it closes with two bits that show how thoroughly the men’s friendship has cemented. The first has them decamping to a rowdy roadhouse after Shirley has been refused admittance to the all-white dining room at the posh place he’d been scheduled to perform; Shirley, of course, mounts the stage to play some classical showpieces before joining in on some jazzy riffs.

The second finds the two driving northward in a blinding snowstorm, so that Tony can make it back home in time for Christmas dinner with his family. If it makes you think back to “Planes, Trains & Automobiles,” you’re probably not far from what Farrelly intended.

The comparison is an apt one, because Mortensen and Ali work as well together as Steve Martin and John Candy did in the earlier movie, the former offering a thoroughly winning turn that involves not only putting on extra weight but a convincing accent and manner totally unlike his own. And though his is the showier part, Ali is equally impressive embodying a man of impeccable grace under demeaning circumstances—mixed with an understanding of his own worth and a touch of neediness. Farrelly is wise to have given them free rein, and they respond with a degree of interplay that any of the great old comic teams might have envied. This is basically a two-hander—Cardinelli is the only other member of the cast who gets any real chance to build a character; but though the rest of the supporting players are doing one-note figures, they’re mostly well chosen.

Farrelly’s approach throughout is certainly not subtle, but it’s considerably more restrained than his joint previous work with brother Bobby. Good period detail from production designer Tim Galvin and costumer Betsy Heiman, nice cinematography by Sean Porter and smooth editing by Patrick J. Don Vito round out a strong technical package, while Kris Bowers’ music doesn’t opt for a crudely bouncy route.

The Green Book, incidentally, was a volume published for some three decades offering black motorists advice on where they would be able to stay and eat along the road without getting hassled—and places to avoid at all costs. “Green Book,” on the other hand, will prove a welcome venue for everybody, though like so many Hollywood dramadies about racism its soft-pedaling of the subject has more than a little contemporary smugness about it.