“Dada,” the sprawling carnival of a show that will open Sunday at the Museum of Modern Art, is an explosive eye-opener. The exhibition, which began at the Pompidou in Paris and traveled to Washington’s National Gallery, is the first major museum show in this country devoted exclusively to Dada, the reactionary, avant-garde art movement born out of artists’ and poets’ responses to the horrors of a mad, modern, war-torn world. It could not have arrived in New York at a better time.

The show comprises more than 400 works by nearly 50 artists. Surveying Dada in Zurich, Berlin, Hanover, Cologne, New York, and Paris, from 1916 to 1924, it includes paintings, drawings, collages, sculptures (some of which are mechanical), graphic design, sound recordings, theater props, puppets, photography, and film.

Much like the movement itself, “Dada” is an uneven mix of works that range from brash or humorous to poetic or puzzling. It is heavy on the usual Dada suspects: such overrated artists as Marcel Duchamp, Max Ernst, Francis Picabia, Otto Dix, and George Grosz. Yet even now, 90 years later, the best works feel fresh. And some of them still have the power to provoke.

The anarchic roots of Dada, which is essentially a Romantic and Expressionistic movement, go at least as far back as Manet’s “Dejeuner sur l’herbe” (1863), one of the first paintings to incorporate shock as a viable tool for the artist. Dada was founded at a cafe in Zurich, the Cabaret Voltaire; its name was supposedly chosen at random out of a French-German dictionary. “Dada,” which is French for “hobby horse,” was also the name of a popular soap and hair tonic; it means “yes, yes” in Romanian, “there, there” in German, and, of course, “papa” in English.

Although Dada was subsumed by Surrealism in the 1920s, its spirit never truly died – especially in America, where we seem to have a bent for the outrageous and the irreverent. Dada was born again (via Duchamp) during the 1950s, in Pop Art works by Robert Rauschenberg and Jasper Johns, and, later, in performance art, guerrilla tactics, and an endless stream of variations on Duchamp’s “Readymades.” In various postmodern forms, neo-Dada is still going strong, riling viewers both here and abroad.

Much of the current art world falls on one side of Dada or the other. You are either against the Dadaist idea that art can be anything at all as long as it wears the badge of absurdity, challenge, irrationality, and irreverence – or you believe that Dadaist art opened a Pandora’s box that voided all previous art movements and justifies the anything-goes spirit of the contemporary art world. “Dada,” the exhibition, has the power to upset both sides of the Dada debate.

What this stupendous collection of works makes clear is that Dada was not merely a onetrick Duchampian pony summed up in the “Readymade,” the blind embrace of chance, and the reactionary assault on society, consumerism, and established artistic tradition. Art movements never come down to one artist, and certainly not to one idea.

Dada, in fact, was various, rich, and independent-minded – and some of its artists were extremely talented and inventive. It may have been fueled by a propensity for chance, nonsense, and shock, but its art was almost never nonsensical. Rather than merely attacking artistic tradition, the best art of the movement revitalized that tradition with newfound intensity and new forms such as abstraction, collage, film, and photomontage.

Kurt Schwitters, who made small Cubist collages out of the ephemera and detritus of the street, firmly established that trash could be art; more important, however, he transformed garbage into magical chamber works. Hans Arp’s amazingly airy and beautiful abstract collages and painted wooden constructions were made, in part, by the laws of chance. Yet these masterpieces make startlingly clear that chance is only one of many actions responsible for the creation of a work of art; only a master and a poet, one who knows how to edit and discern, can embrace chance in his work with success.

Viewing the greatest works in “Dada,” you feel the energy and excitement of artists grappling not only with new forms and media but with a new era. The beautiful and innovative collisions of word and image in the masterful graphic designs of John Heartfield, Raoul Hausmann, Hanna Hoch, Schwitters, and Arp put us at the apex of man confronting his modernity. So, too, do Man Ray’s dreamy, soft-focus photographic works and Fernand Leger’s abstract film “Mechanical Ballet” (1924), a kaleidoscopic, geometric montage of man and machine. Even Duchamp’s “Fountain,” the readymade urinal placed out of its context, comes across as one of the many stars that make up the larger universe of the Dada movement.

The one problem with MoMA’s installation, as opposed to the one at the National Gallery, is that it singles out Duchamp as Dada’s compass. I saw “Dada” in Washington before I saw it in New York, and it was a very different exhibition. That show was installed in a more or less linear fashion, by country, and somewhat chronologically. (Duchamp himself followed a similar principle when he installed a Dada exhibition at the Sidney Janis Gallery in New York in 1953.)

The Washington show began in a dark room, where a montage of silent World War I documentary films was being shown. Although the films – of women making bombs, of bombs exploding, of soldiers marching, of soldiers exploding, of a disfigured soldier being fitted for a prosthetic face – are a little heavy-handed, they set the tone and context for the Dada movement. Viewers in Washington watched in silence, and with reverence, and then they entered the exhibition, as if looking for clues to how, exactly, these artists had responded to such horrors.

MoMA’s curators, Anne Umland and Adrian Sudhalter, in true Dadaist spirit, have taken a different course. Their installation downplays the war films, so that no real context is established. The MoMA exhibition, which has two entrances and no assigned exit, is a kind of circular, free-for-all circus in which each city’s art flows without boundary into the next. You can enter the exhibition through either the “New York” section (the customary entrance to MoMA’s galleries) or that of “Zurich,” MoMA’s customary exit.

The centerpiece of the New York section is an altar to Duchamp. His “Readymades” – including “Bicycle Wheel,” “Bottlerack,” “In Advance of a Broken Arm” (a snow shovel),”Trap” (a coat rack), “Hatrack,” and “Fountain” – establish Duchamp as the belle of the Dada ball.

At the entrance to the Zurich section, we are greeted by a dozen Sophie Tauber-Arp marionettes created for Carlo Gozzi’s play “King Stag” (1918). Though wonderful as objects, these are not Tauber-Arp’s greatest works, especially seen out of context. They overpower her masterpieces in the show: the abstract weavings and collages, some of which she did with her husband, Hans Arp, and her painting “Untitled (Triptych)” (1918), a geometric abstraction in muted browns, blues, oranges, and grays that is one of the strongest paintings hanging at MoMA.

By book-ending the exhibition with Duchamp’s “Readymades” and Tauber-Arp’s marionettes, MoMA’s curators focus our attention, from the outset, not on works of art but rather on process and performance. This thesis reduces the sheer range of art on view to a narrow and pat response to the Dada movement. Despite MoMA’s revisionist agenda, works by such artists as Arp, Tauber-Arp, and Schwitters demonstrate that Dada was much more than a urinal out of context.

From June 18 until September 11 (53 W. 53rd Street, between Fifth and Sixth Avenues, 212-708-9400).