It’s been five years since we got “Shaun of the Dead,” the last really terrific zombie comedy to reach a wide audience, and I’d say we’re overdue for another one. And lookee here, stumbling up the path is “Zombieland,” a deliriously funny and cheerfully gruesome tale of post-apocalyptic mayhem from first-time director Ruben Fleischer.

Zombies have already wiped out most of America when the film begins, and a scrawny college student played by Jesse Eisenberg is trying to get from Austin to his hometown of Columbus to see if his parents survived. In narration, he tells us how a nerd like himself has managed to outlast nearly everyone else. For one thing, he already had a lot of phobias and seldom left the house anyway, so dodging zombies comes easily. For another thing, he’s methodical, with a list of rules he adheres to rigidly. Rule number one for surviving the zombie apocalypse? Cardio. Never underestimate how important it is to be able to outrun the living dead.

On the road he meets a fellow traveler who’s older, tougher, more awesome, the kind of guy who not only kicks a** and takes names but would actually phrase it that way, too. He’s played by Woody Harrelson. He doesn’t like to learn the names of his fellow non-zombies, lest he get too attached. He calls our nerdy hero Columbus, on account of where he’s trying to get to, and identifies himself as Tallahassee, for the same reason.

Tallahassee and Columbus are your standard odd couple, if your standard odd couple bickers between volleys of gunfire aimed at flesh-eaters. (When Columbus corrects him on the fact that penguins don’t live at the North Pole, Tallahassee says, “Do you want to feel how hard I can punch?”) Columbus has gotten pretty good at killing zombies himself, but he’s in awe of his new companion’s skills: “When Tallahassee goes Hulk on a zombie, he sets a new standard of not-to-be-f*****-with.”

The two run into another pair of road warriors, sisters Wichita (Emma Stone) and Little Rock (Abigail Breslin), their names supplied once again by Tallahassee. Everyone has a policy of not trusting anyone, though of course the moral to this sweet little fable will be that life isn’t worth living if you don’t have someone to live it with.

The four also encounter a very cool and very famous Hollywood celebrity, appearing as himself in a brilliantly funny cameo. Knowing who it is won’t ruin anything — you can look at the film’s Internet Movie Database page if you want to — but you might enjoy the surprise. Either way, it’s audacious and loopy and original.

Friendship, camaraderie, snark, and the relentless mowing down of zombies: This is why motion pictures were invented. Some zombie films skimp on the kills, but not “Zombieland”! No sir! Fleischer (working from a screenplay by Rhett Reese and Paul Wernick) indulges the audience with abundant blood and gore, allowing the characters to stumble across far more weapons and ammunition than is plausible in the interest of keeping the bullets flying.

The action eventually leads to an amusement park, an altogether fitting place for a carnival-ride movie like this one. Eisenberg, a more angular version of Michael Cera, might seem an unlikely movie star if you haven’t seen his work in “Adventureland,” but his prim, dorky persona is perfect for Columbus. He’s well matched with Harrelson, whose exuberance makes the happy-angry Tallahassee a nonstop source of delight, the kind of character you’d say steals the show except that he’s already the co-lead and thus part owner of the show.

“Zombieland” doesn’t add anything new to the zombie genre (nor, for that matter, to the comedy genre), and its story is extremely simple, almost to a fault. On the other hand, it’s fast-paced, clever, and filled with inventive details. It deserves to become a midnight-movie cult classic. If it doesn’t, that means the zombies win.

(By the way, as long as we’re on the subject: It never made it to theaters, but the 2008 high school zombie comedy “Dance of the Dead” — think John Hughes meets George Romero — is extremely entertaining and worth a rental. It was a big hit at South By Southwest last year. Some of us saw it twice.)

B+ (1 hr., 25 min.; R, abundant harsh profanity, abundant gory violence, brief partial nudity.)