The cast of the “The Book of Mormon.” (Joan Marcus)

Don’t believe what they say. Money can buy happiness.

It’s yours for the price of a ticket to “The Book of Mormon.” And if you’re already in possession of one, then you’ve wisely secured a seat in the premier-class cabin of delirium.

The brainchild, you may have heard, of “South Park” provocateurs Trey Parker and Matt Stone and “Avenue Q” co-conspirator Robert Lopez, “The Book of Mormon” feels as fresh and frisky and incandescently outrageous in the Kennedy Center Opera House as it did two years ago when it debuted on Broadway. That coming-out earned it a slew of Tonys, among them the statuettes for best musical, direction, score and book.

The touring cast, led by Mark Evans as Elder Price, the brazen young missionary with an ego as vast as a tabernacle choir, and Christopher John O’Neill playing Elder Cunningham, the all-time king of underachieving misfits, does this irreverent roasting of sacred cows proud. And with superb support from Samantha Marie Ware, as a dewy Ugandan with visions of Salt Lake City dancing in her head, and Grey Henson, portraying a Mormon believer bursting to spring from the closet, the farcical team proves to be absolutely first-string.

You’ll not only laugh; you’ll also marvel at the skill with which this show is constructed. Yes, the jibes descend into the juvenile, and the jokes at the expense of religion, AIDS and Third World poverty may compel you to wonder how that sweet-looking older couple at the end of your aisle is taking to all the seemingly blasphemous profanity. But the surprising thing about “Book of Mormon” is that despite all its nihilistic swagger, it’s a musical with a soul.

Mark Evans in the first national tour of “The Book of Mormon.” (Joan Marcus)

It’s also as sturdily assembled as any of those airtight musicals of yore, the ones that Parker, Stone and Lopez pay homage to in their tuneful score. The hilarious Act II number, “Joseph Smith American Moses,” performed by the Ugandan villagers newly swept up by the story of Mormonism, owes an obvious debt to Rodgers and Hammerstein’s “The King and I” and its Siamese reinterpretation of Harriet Beecher Stowe, in “The Small House of Uncle Thomas.” Other sharp production numbers, such as “Spooky Mormon Hell Dream” and the utterly inspired lampoon of psychological denial, “Turn It Off,” could have come from Mel Brooks’s playbook.

They’ve all been packaged with optimal attention to momentum. Glance at your watch at the start of the opening song, “Hello,” a charmingly withering paean to door-to-door proselytizing, because it will be the last time you’ll remember to. Act I barrels breathlessly from one smart song to the next and the next, under the direction of Parker and choreographer and co-director Casey Nicholaw.

The musical’s underlying thematic presumption is that the stories of the Bible are not meant to be taken literally. This could play like irritating, elitist snark — if it all weren’t presented with such an embracing sense of fun. The show intersperses in elders Price and Cunningham’s excellent African adventure several tongue-in-cheek dramatizations of the story of Joseph Smith, 19th-century founder of the Latter-day Saints movement. You laugh, in part because the storytelling has that “Hey, wait a minute!” quality, the kind that might have occurred to you back in Sunday school, listening to stories of miracles that had to be accepted on faith.

“I love all these Mormon stories!” a villager declares. “They are so f---ing weird!” Admittedly, Elder Cunningham, a Mormon with an arm’s-length relationship with the truth, does tend to add Ewoks and starships to the stories he recounts for the village, and it’s these embellishments that win the villagers over. The episodes do not seem intended to shake anyone’s faith. They focus a caustic comic lens on the odd ways in which the spiritual is sometimes translated into digestible imagery. To underline the point, there’s a wonderful moment near the end of the show, when one of the Ugandan villagers reveals how less than gullible they’ve all been all along.

The emotional weight of “The Book of Mormon” is borne by the relationship between the condescending Price — the missionary equivalent of a mean girl — and the desperately needy Cunningham. They’re “Mormon’s” answer to Abbott and Costello, and they have to come across as endearing to us as they are abrasive to each other. With his lean, scrubbed good looks and athletic dancing, Evans is a splendid inheritor of the part from Broadway’s terrific Andrew Rannells. Like Rannells, Evans is able to convey Elder Price’s messianic self-belief as a positive attribute, and his rendition of what may be “Mormon’s” best song, “I Believe,” communicates the number’s priceless sense of irony.

Trying to replicate what the great clown Josh Gad achieved on Broadway would be silly. (Like Rannells, Gad was robbed of the Tony.) So O’Neill takes the character of Elder Cunningham in a slightly less oafish direction, and it pays off on the softer side of the musical. Gyrating like a lounge lizard half his size, O’Neill displays a surprising showmanship in the Act I finale, “Man Up,” and his duet with Ware’s Nabulungi in Act II’s double-entendre song, “Baptize Me,” is gently persuasive.

In the characters’ evolving alliance, Evans and O’Neill manage to forge an affecting friendship. How they seal a bond gives “Mormon” the heart it admirably seeks.

Ware is a beguiling presence in the poignant “Sal Tlay Ka Siti”: she dreams of a paradise in Utah, where “There’s a Red Cross on every corner/With all the flour you can eat.” And the ensemble of Ugandan villagers, pleasingly led by Kevin Mambo’s Mafala Hatimbi, at all times brings astuteness to the satire. (Designer Scott Pask’s rendering of their misery of a village is, to say the least, a revelation.)

“The Book of Mormon” does evince a strange fixation with “The Lion King,” a joke that it overplays. But really, it’s fruitless to quibble with a piece of this entertaining caliber. It is the kind of evening that restores your faith. In musicals.

The Book of Mormon

Book, music and lyrics by Trey Parker, Robert Lopez and Matt Stone. Directed by Casey Nicholaw and Parker. Choreography, Nicholaw; sets, Scott Pask; costumes, Ann Roth; lighting, Brian MacDevitt; sound, Brian Ronan; music supervision and vocal arrangements, Stephen Oremus. With Derrick Williams, Mike McGowan. About 2 hours 20 minutes. Through Aug. 18 at the Kennedy Center. Visit or call 202-467-4600.