An adolescent odd couple bond over punk rock in “The House of Tomorrow,” a pleasantly quirky adaptation of Peter Bognanni’s novel by first-time writer-director Peter Livolsi, which employs a fine cast to sidestep most of the afterschool-special pitfalls the material invites.

Asa Butterfield uses his skill at playing awkward and quizzical—which he earlier demonstrated in “A Brilliant Young Mind” (also known as “X+Y”) and “The Space Between Us”—as Sebastian Prendergast, a sheltered sixteen-year old who has lived most of his life in a geodesic dome outside Minneapolis with his grandmother Josephine (Ellen Burstyn), a disciple of Buckminster Fuller who uses their home to introduce visitors to her master’s ideas. Home schooled and as devoted to Fuller’s theories as his grandmother, Sebastian has had little contact with the outside world.

One day a group of youngsters from a Lutheran church, led by Alan Whitcomb (an amusingly laid-back Nick Offerman), tours the place. Alan’s son Jared (Alex Wolff) challenges Josephine about the reasonableness of Fuller’s belief in the possibility of human progress, and she suffers a minor stroke, leading Alan to accompany her and Sebastian to the hospital. Jared goes along, and he and Sebastian strike up a conversation, at one point sharing some punk rock on Jared’s phone. Sebastian is hooked, and Alan invites him to visit their house sometime.

Jared, you see, needs some friendship, because he’s rebelling against the structures imposed by a recent heart transplant—a regimen Alan is insistent on his following. Jared’s only joy is in practicing the guitar up in his room. When Sebastian shows up unannounced, he’s initially annoyed, but is soon won over by the shy kid’s newly-found passion for the music he loves. Before long Sebastian is strumming on the guitar as well, and the two will plan on starting a band, a scheme that involves Sebastian borrowing another instrument from the church without Alan knowing.

Naturally Sebastian’s absences from the dome cause Josephine to wonder about what he’s up to, and lead to a breach between them. Eventually Alan will take him in, but at the same time he’s concerned that allowing the boys—who now refer to themselves as “The Rash,” a decision that’s probably their most significant achievement toward becoming a real band—to perform at the church talent show will exhaust his son, who has already suffered a crisis after ceasing to take his medication. That leads to their decision to take drastic action to find a performance space.

This could easily be the stuff of a Nickelodeon cable movie, and in truth there are moments when it threatens to fall into that trap, most notably in the last reel, where things turn out well in a whole variety of unlikely ways. That it never goes completely off the rails is due largely to the charm exuded by Butterfield and Wolff, and the chemistry they have together. But Offerman’s concerned but somewhat clueless dad is a plus as well, and Maude Apatow adds a solid turn as Jared’s sister, who at first acts like a typically surly sibling but turns out to be much more supportive than she seems. Michaela Watkins contributes a poignant note in a virtual cameo as Alan’s heavy-drinking wife, who is living apart from the rest of the family.

And then there’s Burstyn, who delivers a nicely nuanced performance as a true Fuller believer. A brief black-and-white clip of her with him occurs at one point among the archival footage assembled as an educational tool for Josephine’s lectures (the narration is provided by Fred Armisen, employing a bland professorial voice); it’s no technical trick, since Burstyn actually knew and worked with him in earlier days. The picture, shot in Minnesota at a dome house in Dayton inspired by Fuller’s ideas (and partially funded by the Film Program of the Sloan Foundation, which promotes movies about scientific progress), boasts nice cinematography by Corey Walter. The other technical work is solid as well, and Rob Simonsen provides an agreeable score, complemented by plenty of punk numbers.

“The House of Tomorrow” may not break much new narrative ground, but it treads fairly familiar territory with a nicely light touch, adding some inventive tweaks along the way. And the excellent cast makes it go down easily.