Halfway through this affable, inspired grab bag of a comedy, it hit me that what I was watching wasn’t merely a good movie but the Greatest TV Adaptation Ever Made. OK, the bar wasn’t exactly high. Nonetheless, cowriters Jonah Hill and Michael Bacall deserve credit for their discovery that the secret to success in this genre is keeping the source material’s title and premise, then losing everything else that made it a hit way back when.

21 Jump Street is likely to prove all but unrecognizable to anyone who remembers the late-’80s television series on which it’s based. As directed by Phil Lord and Chris Miller (Cloudy with a Chance of Meatballs), the film is very much an Age of Apatow exercise, a cinematic tossed salad of raunch, drugs, pop-culture parody and unabashed warmth. While I never saw the TV show, I am fairly sure it had fewer penis jokes.

Hill costars with Channing Tatum, an actor not known for his comedic gifts. One of the movie’s many pleasant surprises, as it turns out, is that he’s a natural. The two play rookie cops assigned to an undercover operation. As their supervisor — Nick Offerman from “Parks and Recreation” — explains, “The police have run out of new ideas. All they can do is recycle crap from the ’80s and hope nobody notices.” Their assignment: masquerade as high school students and find the source of a dangerous new recreational drug (“It’s killing white kids, so people care”).

The notion that Hill and Tatum could pass for teenagers is hilarious, and the movie has a lot of fun with that preposterousness. Funnier still is the idea that they could be brothers, but that’s the boneheaded ruse their supervisors concoct. Hill is supposed to be Brad, an overachieving dweeb, while Tatum’s planned secret identity is Doug, ladies’ man, star athlete and straight-F student. But, just as he can never quite manage to memorize the Miranda rights, he spaces out in the principal’s office on their first day and gets it backward.

Which works out just great for Hill’s character. He gets to relive high school as one of the popular kids. His partner finds himself in equally unfamiliar territory — namely, AP chemistry. The script mines the mix-up for maximum laughs.

My favorite sequence follows the cops’ initial encounter with Eric (Dave Franco), the ecology-minded teen drug lord. He agrees to sell them each a hit as long as they take it then and there to prove they’re not narcs. The subsequent 20 minutes are the most gut-busting I’ve seen on screen since Bridesmaids. Hill’s kite-high track meet is an instant classic, and I loved the Limitless-inspired bit in which, peaking on the mind-altering substance, Tatum strides up to a whiteboard, slashes numbers on it feverishly and throws down his marker, shouting, “Fuck you, science!” Upon which the camera zooms in on his creation, a maniacally scrawled jumble of 4s.

The movie offers lots of equally surreal moments, and its pacing is a thing of beauty. There isn’t a dull patch. Bacall and Hill demonstrate consummate mastery in blending disparate tones and themes. One minute 21 Jump Street ruminates on how the high school experience has changed over the past decade. (Tatum misses the good old days when dumb jocks ruled and blames the triumph of sensitivity on “Glee.”) The next, the film spoofs action-movie conventions, as in the highway chase throughout which nothing that would normally blow up agrees to blow up.

Of course, it’s also one hell of a love story. And I’m not talking about the borderline-wrong crush between Hill and an underage student (Brie Larson). The real attraction here is between Brad and Doug. The movie takes bromance to new heights, in the process illustrating with a loopy brilliance precisely what’s so funny about police, love and understanding.