Kim Kardashian struggled to contain herself — literally — at the debut of Sofia Coppola and Valentino’s “La Traviata” on Sunday. At the Rome Opera House, curvy Kardashian was constantly adjusting.

“Her cup had runneth over,” said a source. “She spent the whole time adjusting her bust. One boob kept popping out, in front of all the Italian counts and countesses.”

Kim Kardashian and Kanye WestGetty Images

On the red carpet, the star also gamely battled her dress’ slit to shield some Spanx from peeking through. But besides Kim’s sartorial setback, “you’ve never seen a more beautifully dressed group of people,” said a guest.

Glam attendees included Keira Knightley, Monica Bellucci, Eugenie Niarchos, Ginevra Elkann, Bianca Brandolini, Nacho Figueras, Valentino — who created costumes for the production with Maria Grazia Chiuri and Pierpaolo Piccioli — and Giancarlo Giammetti.

“There was a time people were excited to see the royals,” one aristocrat was heard sighing at the elegant event.

“Now they just trip over us to get to Kim Kardashian.” A source observed: “Kim and [husband] Kanye West were sitting behind Elizabeth Hurley and people were just climbing over Liz to get to Kim. Not to talk to her, just to stare at her.”

Among those applauding in a standing ovation were proud papa Francis Ford Coppola and auteurs Bernardo Bertolucci and Paolo Sorrentino.

At an afterparty, Knightley was dancing “in front of the stage” as her rocker hubby, James Righton, performed. We hear the pair planned to stay in Italy as “It’s the first time they’ve been away together since having their baby” last June. For any other stragglers, we hear Giammetti even arranged a private tour of the Sistine Chapel. He’d also thrown a lavish dinner Saturday.