“It Follows” opens Friday at Point, Eastgate, Star Cinema and Sundance. R, 1:33, three and a half stars out of four.

Remember, kids, when you have sex, you’re having sex with every person they’ve ever had sex with. And also with a demon stalking all of you.

David Robert Mitchell’s brilliantly creepy horror film “It Follows” opens with what could be a scene from any other horror movie. A frightened teenage girl in negligee and high heels runs from an unseen threat across her placid street in the Detroit suburbs.

But Mitchell films it in a single tracking shot, from an omniscient distance, so we have no clue what the girl is afraid of. She almost seems silly clunking around in those heels — until Mitchell abruptly cuts to the next morning, her mangled body on the beach.

“It Follows” isn’t like almost any horror film you’ve seen. In its original premise, in its fresh and masterful approach to invoking a feeling of dread in the audience, and in its depth of characterizations, “It Follows” is excitingly, unnervingly different. Imagine if Richard Linklater made a horror film, and made it really, really well.

The premise is ingenious — teens pass a curse from one to the next like a chain letter, through having sex. The last person to have it becomes the target of a slow-moving, unwavering creature who can look like anybody — an old lady, a naked woman, your father. It zeroes in on you, takes its time, and never, ever stops until it kills you. The only way to shake it is to have sex with somebody else, and pass the curse forward.

Jay (a terrific Maika Monroe) is another suburban girl who gets cursed by a handsome guy from another town, and frantically tries to stay one step ahead of a deadly menace that only she can see. And she also has to consider whether to take the one definitive step towards saving herself — passing the curse to somebody else. (Interestingly, I don’t think anybody in the film actually uses the word “sex” or any of its more vulgar synonyms.)

Mitchell masterfully uses empty spaces, slow pans and pull-ins, and reaction shots to suggest where the creature could be, hiding in plain sight. In one scene, at a busy high school, Mitchell turns the camera in a slow 720-degree pan, and there’s one student we spy in the crowd who might be the creature, walking towards us. But we don’t know for sure.

Mitchell evocatively uses the Detroit setting, moving from placid suburban streets to abandoned houses and hollowed-out factories, to suggest the permeable line between innocence and evil. The Tangerine Dream meets John Carpenter soundtrack is also exquisitely creepy, the eerie synths sometimes dissolving into a wail of discordant noise, as if the presence of the creature nearby is corrupting the music itself.

The premise of “It Follows” is not only an ingenious way to deliver thrills (and deliver them on a budget), but allows Mitchell to explore themes involving adolescence and the transactional nature of sexuality, what is gained and what is given away. Themes of childhood lost reverberate through the film — the teens pass the time hiding from the creature talking about what they used to do as kids, and comic books, juice boxes, and breakfast cereal boxes appear as relics of lost innocence. The creature could represent encroaching adulthood, this otherness that adolescents can’t escape.

But Mitchell (who made a terrific slice-of-life teen drama called “The Myth of the American Sleepover”) braids these themes carefully within its genre shocks and pleasures. We seem to be enjoying a renaissance of horror films like “The Babadook,” “The Guest” and even “Under the Skin” that elevate the genre with smarter writing, better performances and deeper themes. Add “It Follows” to the top of that list.