NEW YORK — “Hair,” the legendary 1960s American Tribal Love-Rock Musical, has made the jump from a summer Central Park engagement to Broadway with all its exuberance intact — and more.

If you want to know why this joyous revival, which opened Tuesday at the Al Hirschfeld Theatre, is so successful, you need not look any farther than the show’s first-act finale. No, not its brief display of nudity, but what is happening around it.

In this moment of Dionysian frenzy, creators Gerome Ragni, James Rado and Galt MacDermot have neatly encapsulated the musical’s themes. As the hippie tribe chants of beads, flowers, freedom and happiness, Claude, one of show’s leads, poignantly sings, “Why do I live, why do I die, tell me where do I go, tell me why.”

Director Diane Paulus has done an extraordinary job in illuminating these two conflicting ideas — the clash of spontaneity and the search for identity — ideas that pulse through much of the evening. Paulus, along with choreographer Karole Armitage, are superb guiding spirits, galvanizing an energetic, appealing cast that has gotten better and better since the Public Theater’s outdoor production last year.

The characters may be on the brink of chaos, with a social, political, racial and sexual revolution swirling around them, but Paulus never lets the celebration get incoherent. If anything, she has refined the production’s clarity. Not an easy task when the book by Ragni and Rado is cheerfully anarchic and practically non-existent, and the music determined to spin off into a cornucopia of styles.

It’s the songs that have allowed “Hair” to remain popular well into middle age. The parade of hits don’t stop, and MacDermot’s melodies are as infectious as ever. Try not humming “Aquarius,” “Easy to Be Hard,” “Frank Mills,” “Good Morning Starshine” and, of course, “Let the Sun Shine In.” If the songs don’t exactly move the plot forward, they serve as atmospheric reminders of what the show is about, a perfect blending of theatrical and pop.

There’s been a couple of cast changes since the park, and two really strengthen the show.

Gavin Creel, besides possessing a powerhouse voice, brings a sweet-tempered poignancy to Claude, the most anguished member of the tribe. It’s Claude who has the most back story in the show: a conventional, middle-class upbringing in Queens; a total fascination with all things British, expressed in the song “Manchester, England”; and an uneasy sense of duty that eventually gets him drafted and into the Vietnam War. Creel handles it all with assurance.

Caissie Levy, another new addition, nails “Easy to Be Hard,” with a throaty, bitter rendition of the song, a tough-minded cry against negativity, personal and public.

Alums from the 2008 Central Park production remain just as vivid as before, particularly a charismatic Will Swenson as the hedonistic Berger, who outrageously interacts with the audience — as do other select members of the cast. Anyone who does not wish to get involved would be advised not to sit in aisle seats or the front row.

“Hair” was never shy at poking fun at parental figures, whether they are traditional mothers and dads, or anthropologist Margaret Mead, essayed here by a hilarious Andrew Kober. And Megan Lawrence has a fine comic turn as Claude’s disapproving mother.

When the Broadway transfer of “Hair” from Central Park was first announced, there was some concern the absence of an outdoor setting would diminish the musical’s effectiveness, dampen its communal spirit. It turns out, there was no need to worry.

“Hair” looks and feels just fine in the Moorish palace that is the Hirschfeld. Scott Pask’s design — featuring the back brick wall of the theatre — may be minimal, but it allows the show’s terrific band to sit right up on stage.

Besides, when theatregoers enter the Hirschfeld, they are greeted by a shimmering curtain of the plant Earth. Right away, a sense of community reigns, a connection that extends even after the show’s haunting finale – when cast and audience begin dancing together on stage. At age 40-something, “Hair” is the liveliest show in town.