The late Rod Serling is probably smiling if he’s looking down on “10 Cloverfield Lane,” a taut, claustrophobic exercise in tension with a distinctly “Twilight Zone” vibe. It’s being marketed, rather misleadingly, as a sequel to J.J. Abrams’ big found-footage Godzilla-running-amuck-in-NYC picture of 2008. The relationship to that movie is tenuous at best, but the important point isn’t that “Lane” is very different from its nominal predecessor—it’s that it’s far better.

One can’t reveal too much of the plot without spoiling the experience, but it focuses on Michelle (Mary Elizabeth Winstead), whom we see in a largely wordless prologue leaving her fiancé Ben (Bradley Cooper, heard but not seen in a couple of phone messages) and driving determinedly out of the city. Along a deserted stretch of highway she’s in an accident while listening to Ben’s last voicemail, and wakes up in an underground bunker, chained to a cement wall.

Soon Howard (John Goodman) appears with a tray of food, telling her that he’s saved her from a disaster that’s struck the outside world—perhaps an invasion by one of the USA’s many earthly enemies, perhaps something extraterrestrial—that has contaminated the air and left the rest of the population dead or dying. The two of them—along with Emmet (John Gallagher, Jr.), a handyman who helped Howard build his safe, homey, well-stocked cellar—will remain secure as long as they stay where they are and work together to survive.

The big question is whether Howard is, in fact, sane or a dangerous nut job. Certainly his actions could support either view. At times he’s matter-of-fact, even friendly. But there’s a clear note of menace in his manner, and he’s volatile, turning on a dime to become enraged and threatening. There’s also something strange about his references to his daughter, whose clothes he offers to Michelle.

The corollary is whether Michelle should go along with Howard’s house rules or try to escape, perhaps with the aid of the pliable Emmet. The problem is that there’s evidence that Howard is right about what happened outside their little oasis and going out into the world could be deadly. On the other hand, Howard’s demands and outbursts make it possible that it’s equally dangerous to stay under the same roof with him.

It wouldn’t be fair to reveal much more of the plot than that. But certainly Josh Campbell, Matt Stuecken and Damien Chazelle are inventive in constructing suspenseful situations and surprising twists—including a bug one toward the close—and director Dan Trachtenberg and editor Stefan Grube demonstrate considerable skill in framing and delivering the narrative. Except for sequences at the beginning and end, Jeff Cutter’s cinematography happily eschews the jittery, hand-held style of the original “Cloverfield” in favor of steady, straightforward camerawork that concentrates the intensity. Brear McCreary’s score contributes to the mood as well, as do Ramsey Avery’s production design and the sets by Trish Vu and Dave Kelsey.

Of course, none of that would matter much without the dead-on performances. Except for a few instances, Goodman sheds the geniality that has marked much of his past work, fashioning a convincing portrait of a fearsome bear of a man who nevertheless might just be right about what’s happening to the outside world. Winstead, meanwhile, is no mere damsel in distress; in her hands Michelle is a formidable figure in her own right, clever, persistent and willing to go to extremes to do what she believes necessary. And Gallagher makes Emmet an engaging doofus, with a streak of nobility in his scruffy soul. This is a chamber piece: these three carry the picture comfortably, and one glimpses only one other person in the flesh during the course of the entire picture.

“10 Cloverfield Lane” started out as a script for a low-budget indie called “The Cellar,” and some might question whether transforming it into an installment of a big ongoing franchise was the right move; the result does sometimes feel like a “Twilight Zone” episode that’s suffering from a bit of bloat. One can also doubt the wisdom of a final touch that suggests a continuation of the story along a fairly conventional line.

Taken on its own, though, this is an unsettling three-character suspense drama that will keep you guessing.