When learning the plot of “The Peanut Butter Falcon,” a reader may think it’s not a real movie — because no one in their right minds would take such incongruous elements as crab fishing, professional wrestling and Down syndrome and combine them in a heartwarming, Mark Twain-esque comedy-drama.

However, that’s exactly what the writing and directing team of Tyler Nilson and Mike Schwartz have done for their feature debut. And this weird concoction somehow works, thanks in no small part to the acting chops of Shia LaBeouf and the charm of newcomer Zack Gottsagen.

Gottsagen plays Zak, a young man who, like the actor, has Down syndrome. Zak, the character, has no family and lives in a nursing home as a ward of the state of North Carolina. Zak’s roommate is a crotchety old ex-engineer, Carl (Bruce Dern), and the only person in the home anywhere near his own age is his social worker, Eleanor (Dakota Johnson).

Zak escapes from the home, determined to find his hero, a pro wrestler called the Salt Water Redneck (Thomas Haden Church). The nursing home’s operator sends Eleanor out to find Zak before the authorities do. Eleanor, driving the home’s van, follows Zak’s trail, which turns out to be more interesting than she could ever imagine.

The first person Zak encounters after escaping is Tyler (LaBeouf), a down-and-out crab fisherman along North Carolina’s Outer Banks. Tyler spends his time poaching crabs, which gets him beat up by Duncan (John Hawkes), the fisherman who holds the license under which Tyler used to work when it was held by his now-deceased brother, Mark (played, in flashbacks, by Jon Bernthal).

Tyler torches Duncan’s crab traps, and must flee for his life from Duncan and his thuggish underling, Ratboy (played by the rapper Yelawolf). That’s when Tyler finds Zak in the back of his boat. Tyler fears Zak will slow him down, but he ultimately decides to help him on his quest to find the Salt Water Redneck. Thus begins a road trip in which Tyler teaches Zak about living life, and in which Eleanor — who also has a complicated backstory — becomes a reluctant but bemused traveling companion.

As filmmakers, Nilson and Schwartz have a goofy rhythm, letting the story seemingly take the characters at their own wandering pace. This allows for some unforced moments, like when Tyler helps Zak develop his wrestling alter ego (check the movie’s title), or when Zak gets to experience his own wrestling camp (populated by real wrestlers Mick Foley and Jake “The Snake” Roberts). But the stop-start storytelling also leaves some annoying gaps, like the unexplained romantic subplot between Tyler and Eleanor.

Still, “The Peanut Butter Falcon” retains its own peculiar appeal. Like a southern-fried variation on “Rain Man,” Gottsagen’s Zak and LaBeouf’s Tyler have a sweet-and-sour chemistry that propels this curious little road movie further than one would expect.

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★★★

‘The Peanut Butter Falcon’

A weird, but oddly charming, road picture centers on a young man with Down syndrome and a hard-luck drifter.

Where • Megaplex at The Gateway (Salt Lake City), Century 16 (South Salt Lake City), Megaplex Jordan Commons (Sandy)

When • Opens Friday, Aug. 9

Rated • PG-13 for thematic content, language throughout, some violence and smoking.

Running time • 93 minutes