Hard to believe it’s been 40 years since “Stop Making Sense” came out and took its place as one of the best rock-docs ever made. The collaboration between late filmmaker Jonathan Demme (“Silence of the Lambs,” “Something Wild”) and the ’80s punk-art band Talking Heads registers the same immersive lightning-in-a-bottle effect today as it did back when the band was on tour to promote its fifth album, “Speaking in Tongues,” and near the apex of its success. Shot for a mere $800,000 (put up by the band and Demme) over three nights at the Pantages Theater in Hollywood, the need-to-see-that-again (and again) effect is the fusion of tight, judicious editing, visceral camera work and the band’s nonstop, infectiously energetic performance.

David Byrne, the band’s lean, tragically handsome frontman, proves to be something of a conductor of controlled chaos as he spasms rhythmically across the stage and bobs his head with the strange, alluring grace of an ostrich. Then there’s that big, boxy suit that feels stolen from the set of a David Lynch film. As captured, Byrne casts a suave, seductive magnetism akin to contemporary Brian Ferry (whose frenemy and former Roxy Music bandmate, Brian Eno, co-wrote and produced several Heads songs, including the seminal “Once in a Lifetime,” which gets a standout performance in the film) with a shot of Johnny Rotten’s spit-in-your-face punk defiance. Byrne’s own bandmates (they all met at the Rhode Island School of Design in the ’70s) are bassist Tina Weymouth, drummer Chris Frantz (married to Weymouth for 46 years, seven of them before the making of the film), and guitarist-keyboardist Jerry Harrison, all bearing gleeful smiles as they take in Byrne’s intoxicating mania like proud parents beaming over a child’s impish playground idiosyncrasies. Those who find their way into Byrne’s aura of quirk do so with a seamless, natural glide. Most adept are Heads accompanists Alex Weir, a high-kicking blues guitarist, and the killer backup tandem of Lynn Mabry and Ednah Holt, who make the cinematic “Take Me to the Water” – borrowed from the great Al Green – the soulful anthem that it is.

The film’s arc is crafted with care and purpose. The opening sequence renders a drab, open stage, something of an art studio without easels. There’s no risers, amps or instrument setups in sight, and Byrne, in Sperry Top-Siders and a mod suit, ambles out with a boombox and guitar to perform an acoustic version of “Psycho Killer,” the band’s big first album hit. “Have we been sold a bill of goods?” audiences in 1984 must have thought, but then come those snaky, goose-neck jerks that hold you rapt as this dressed-down alternative seeps into the bones. Stage pieces slowly – and furtively – roll out, band members sprinkle in and the lights go down, creating a minimalist, noir ambiance. From frame one, there’s no ebb. Sweat drips and the players achieve a synchronicity notched by the rare few: The Who at the Isle of Wight, or Santana doing “Soul Sacrifice” at Woodstock. One of the great gifts of the film comes when Byrne leaves the stage and Weymouth and Franz’s side project, Tom Tom Club, takes over for “Genius of Love,” a hippity-hop, bluesy rap ditty led by Weymouth, Mabry and Holt. The universally acknowledged highlight is that Eno-produced “Once in a Lifetime” number (though my fave is “Swamp”), in which Byrne, wearing that notoriously boxy suit, chops at his arm and smacks his head back, performing a limbo move that would make the lithest of yogis turn green. The side angle showing Mabry and Holt mirroring him is an aesthetic wonderment, ghostly in composition and ingenious in orchestration.

Among the other all-time best rock-docs, two similarly are collaborations between a celebrated filmmaker and iconic artists: “The Last Waltz” (1978), directed by Martin Scorsese capturing The Band’s farewell concert, and “Gimme Shelter” (1970), in which The Rolling Stones confront the stabbing at their Altamont Speedway concert (meant to be a Woodstock west) under the guidance of the legendary Maysles brothers (“Grey Gardens”). The top five also includes the concert-of-all-concerts, “Woodstock” (1970), which had a young Scorsese aboard as an editor, and “Dig!” (2004), the train wreck rock ’n’ roll parable driven by the mercurially self-destructive behavior of Brian Jonestown Massacre (speaking of the Stones) frontman Anton Newcombe and the band’s feud with The Dandy Warhols. 

• At The Brattle Theatre, 40 Brattle St., Harvard Square, Cambridge; Landmark Kendall Square Cinema, 355 Binney St., Cambridge; Somerville Theatre, 55 Davis Square; and AMC Assembly Row 12, 395 Artisan Way, Assembly Square, Somerville.