Emily Padgett, left, as Daisy Hilton and Erin Davie as Violet Hilton in “Side Show.” (Joan Marcus/Joan Marcus)

Capped by two climactic, heartbreaking songs and two tender, epic performances, the “Side Show” that has been given a new life by the Kennedy Center is an intoxicating experience — a poignant statement about the brutal rite of achieving self-acceptance and a glorious comeback for an important American musical.

The pair of performances that drive the visually vibrant production, which had its official opening Thursday night, are so symbiotically entwined you’d think the two actresses were joined at the hip. Well, in point of fact, they actually are. Erin Davie and Emily Padgett portray Violet and Daisy Hilton, Siamese twins who go from being a tawdry carnival act to celebrated vaudeville stars but never what they truly desire: people seen as separate from their abnormal condition.

In this new version of the 1997 musical, reworked by composer Henry Krieger, book writer and lyricist Bill Russell and director Bill Condon, the distance the sisters travel from a cruel childhood of exploitation has been clarified. The mystical nature of their connection has been deepened, too, via a more concerted consideration of loneliness and freedom, themes that envelop them and many of the other hauntingly conceived “freaks” who fill the Eisenhower Theater stage.

Around the young women, Condon has assembled a superb supporting cast, represented most pivotally by Matthew Hydzik and Ryan Silverman as the show business pros who save, enrich and ultimately devastate the Hilton sisters; and most poignantly by David St. Louis, portraying Jake, the side show “attraction” who becomes the sisters’ stalwart protector and worshipper of Violet from afar.

But it is the sisters themselves — and Davie and Padgett’s remarkable abilities to deliver synchronized performances even as the women reveal dreams at odds with each other — who give this “Side Show” its anguished momentum. Anyone not knocked out by their Act 1 finale, the ravishing “Who Will Love Me as I Am?,” is hereby ordered to have their vital signs checked.

Ryan Silverman, left, Emily Padgett, Erin Davie and Matthew Hydzik in “Side Show.” (Joan Marcus/Joan Marcus)

The number is the proverbial tough act to follow. Still, if Act 2 doesn’t quite activate the tear ducts as frequently as Act 1 does, it offers other major consolations in, among other things, three powerhouse songs, marvelously orchestrated by Harold Wheeler: “A Private Conversation,” in which Silverman’s Terry sings to the woman he can’t have to himself; “You Should Be Loved,” the power ballad that St. Louis’s Jake sings to the woman who won’t have him, and “I Will Never Leave You,” the second of the sisters’ rawly beautiful melodies that, dare I say, may never leave you, either.

The best of the musical’s new songs — and there are 10, full and fragmentary ones — is “Stuck With You,” a novelty song for the vaudeville sister act that now opens Act 2 and features Davie and Padgett in one of the dazzling pairs of identical costumes Paul Tazewell has designed for them. The number, awash in double meaning, recalls the clever pastiche-driven songs in another show-business musical, Stephen Sondheim and James Goldman’s “Follies.” (Another new song, “Ready to Play,” is a first-rate showcase for Anthony Van Laast’s stylish choreography.)

“Side Show” was a succès d’estime on Broadway but a commercial flop, owing partly to the skittishness some audience members felt toward a central aspect of the story: the romantic lives of Siamese twins. Really? The elusive motives and feelings of promoters Terry and Buddy (Hydzik’s role) didn’t help. Condon, who wrote the screenplay for the Oscar-winning movie version of “Chicago” and directed the film of Krieger’s “Dreamgirls,” has seen to it with Russell and Krieger that the conflicts arising in the two men between their business and emotional interests in Daisy and Violet make more sense. This is especially true in the conception of Buddy, whose sexual nature is far better explained, giving more validity to the evening’s pivotal breakdown.

The musical is based on the real-life Violet and Daisy, focusing on their rise as entertainers in the late 1920s and early ’30s, when they appeared in Tod Browning’s exploitational horror classic, “Freaks.” The story of their ghastly childhood in England — rendered as a stark foreshadowing of Browning’s movie — is new to the musical, as is the inspiring visit to the sisters by escape artist Harry Houdini (Javier Ignacio), who imparts to the young women the tools for their own transcendental escape, into their separate consciousnesses. (The idea is later echoed, chillingly, in Terry’s melodic fantasy of having Daisy “for my own,” through the risky intervention of surgeons.)

Daisy and Violet find their real family in the side show, presided over by one of the bona fide monsters who raised them, called “Sir” and played with potent loathsomeness by Robert Joy. This is where the musical opens, as the assortment of “God’s mistakes” who share billing with the Hilton sisters serenade us into their world through the stirring “Come Look at the Freaks.”

It’s a fabulous introduction, heightened by the stunning realization of the 13 or so “freaks.” Goose bumps are raised with the introduction of each, a procession for which the special-effects team deserves plaudits. The costumes are all so evocative that each “freak” merits a mention here: Don Richard’s Reptile Man; Lauren Elder’s Venus di Milo; Ignacio’s Dog Boy; Blair Ross’s Bearded Lady; Kelvin Moon Loh’s Half Man-Half Woman; Brandon Bieber’s Three-Legged Man; Hannah Shankman’s Tattoo Girl; Josh Walker and Jordanna James’s World’s Tiniest Cossacks; Barrett Martin’s Human Pin Cushion, Charity Dawson’s Fortune Teller, St. Louis’s Cannibal King — and most eerily, Matthew Patrick Davis’s Geek.

They are both the VIPs and regular folks of “Side Show.” Because, of course, they are us. Who hasn’t felt the world’s judgmental stare, shuddered at its scornful smirk? Who hasn’t felt like a freak? In a scene at a swanky New Year’s Eve party — adorned by set designer David Rockwell, in one of his many smart scenic touches, with an impressionistic city backdrop — a society dame has the temerity to ask the sisters, “Whatever you are, don’t you want to be normal?” Violet’s reply is a withering putdown: “Whoever you are — don’t you?”

“Side Show’s” rendering of Violet and Daisy as in all ways recognizably “normal” should silence the issue of whether they’re appealing heroines, in this, the boldest and most splendidly realized production by the Kennedy Center since the “Sondheim Celebration” in 2002. And the magnetic, graceful portrayals by Padgett, as fame-seeking Daisy, and Davie, as the comforts-of-home-craving Violet, should mute any reservations entirely. Singly and doubly, they’ll melt your heart.

Side Show

book and lyrics by Bill Russell, music by Henry Krieger. Directed by Bill Condon. Choreography, Anthony Van Laast; sets, David Rockwell; costumes, Paul Tazewell; lighting, Jules Fisher and Peggy Eisenhauer; sound, Kai Harada; special makeup effects, Dave Elsey and Lou Elsey; illusions, Paul Kieve; orchestrations, Harold Wheeler; music direction, Sam Davis; wigs and hair, Charles G. LaPointe. With Derek Hanson and Con O’Shea-Creal. About 2½ hours. Tickets, $45 to $130. Through July 13 at the John F. Kennedy Center for the Performing Arts, 2700 F St. NW. Visit www.kennedy-center.org or call 202-467-4600.