“I was in Rhode Island the first time I saw ‘Airplane!’ ” recalled Peter Farrelly, who co-directed “There’s Something About Mary” and many other slapstick comedies with his brother, Bobby. “Seeing it for the first time was like going to a great rock concert, like seeing Led Zeppelin or the Talking Heads. We didn’t realize until later that what we’d seen was a very specific kind of comedy that we now call the Zucker-Abrahams-Zucker school.”

Peter Farrelly and a writing partner, Bennett Yellin, were so enamored with “Airplane!” that they contrived to get a comedy script (still unproduced) into the hands of David Zucker, who liked it enough to give them their first Hollywood writing job. “I’ll tell you right now,” Peter Farrelly said, “if the Zuckers didn’t exist, there would be no Farrelly brothers.”

Back in 1979, when “Airplane!” was being shot on Universal’s back lot in Los Angeles, it didn’t seem like a potential blockbuster. The three Wisconsin-born filmmakers were rather amazed that anybody would give them a budget — and $3.5 million at that — to make such a lark, one that had no big stars. A follow-up to their 1977 cult film “The Kentucky Fried Movie,” which they had written, this was an extended riff on “Zero Hour!,” a glum thriller from 1957 about an imperiled aircraft that set the template for the next half-century’s worth of disaster pictures.

The plentiful pop cultural references and anything-for-a-laugh attitude of “Airplane!” recalled early films by Mel Brooks ( “Blazing Saddles” ) and Woody Allen ( “Bananas” ). But its velocity and density were new. Every scene was packed with surreal, often faintly metafictional sight gags (including a supporting turn by the N.B.A. giant Kareem Abdul-Jabbar as a co-pilot who denies that he’s really Kareem Abdul-Jabbar, and a cameo by Ethel Merman playing a psychiatric patient who thinks he’s Ethel Merman). And the film proudly served up jokes so astoundingly corny that they somehow managed to circle around the bend and become hilarious. (“Surely you can’t be serious.” “I am serious — and don’t call me Shirley!”)

At the same time “Airplane!” wasn’t just a collection of bits. The narrative hewed closely to that of “Zero Hour!,” and if you can factor out all the silliness — no small feat with a movie that segues from a “Casablanca” -inspired romantic flashback to a “Saturday Night Fever” -like dance number — what remains is a compact, even classical piece of filmmaking.