Cameron Crowe ran into Elton John last year at a party thrown by David Geffen. “I hear you’re doing a musical version of ‘Almost Famous,’” John said. “I love Tom Kitt” – Crowe’s collaborator – “but you’d better use ‘Tiny Dancer!’”

“Hell, yes — and thank you!” Crowe replied, then skedaddled, lest John have second thoughts.

“Tiny Dancer” is right where it should be in “Almost Famous,” which opened last week at San Diego’s Old Globe theater. But this is no jukebox musical: Crowe and Kitt, who won a Pulitzer for “Next to Normal,” have written 20 new songs that, judging from the reviews, sit nicely beside the classics by David Bowie, the Allman Brothers, Deep Purple, Joni Mitchell and Cat Stevens that flit through the show.

“Most of the songs we wrote are for Stillwater, so they’re midlevel songs,” Crowe says of the fictitious band of both the musical and the 2000 movie. “But we’ve tried to craft them so they keep you in the time frame of the movie and the era.”

Thanks to the new songs, “Almost Famous” feels at once “familiar…and refreshing,” Variety said. The Los Angeles Times called the production “as pleasing as a free and easy 1970s rock classic.”

The powers that be on Broadway — the Shuberts, the Nederlanders and Jujamcyn — are already scrambling to find a theater for the show. (The Barrymore might be the ticket if “The Inheritance” doesn’t pick up at the box office.) The plan, production sources say, is to bring the show here before the Tony cutoff in May, setting the stage for one of the most competitive Best Musical races in years — a field that could include “Moulin Rouge,” “Tina: the Tina Turner Musical,” David Byrne’s “American Utopia,” Alanis Morissette’s “Jagged Little Pill” and Bob Dylan’s “Girl From the North Country.”

Set in the early 1970s, the autobiographical “Almost Famous” is about a teenage journalist’s travels with a freewheeling rock band. (Crowe was just 16 when he followed the Allman Brothers and wrote his first cover story for Rolling Stone.)

Crowe says that plenty of theater people approached him about turning “Almost Famous” into a musical, and he even kicked around his own version. “But in the end, it never felt personal enough,” he says. “It didn’t hurt the way you hurt when you hear a new Joni Mitchell song for the first time and you feel you’re the only one in the world who understands it.”

Then he met British director Jeremy Herrin (“Wolf Hall”), who outlined an idea for the show that would retain the tenderness and intimacy of the movie. Kitt came on board and, says Crowe, “we’ve been this three-headed musical theater geek ever since.”

Crowe, 62, grew up in San Diego, not far from the Old Globe. His mother loved the theater — she cherished the memory of seeing Marlon Brando in “A Streetcar Named Desire” on Broadway — and often took him to see shows.

“Around the time I was discovering rock music, she was trying to sell me on Stephen Sondheim,” he says. He fell in love with one Sondheim song, “Barcelona,” that sad and wistful love duet from “Company.” He and Kitt pay tribute to it in “Almost Famous” with the song “Morocco,” about flickering love. “When Tom first played me the melody, it felt like a distant cousin to ‘Barcelona,’ ” Crowe says.

Critics have singled out “Morocco” as one of the highlights of the musical.

But the show has the blessing of someone more important to Crowe than the critics: Joni Mitchell, who suffered an aneurysm a few years ago and no longer performs, attended its opening night. At a reception after the show, Crowe introduced her to his director. She took Herrin’s hand and said, “It’s better than the movie.”

“I was ecstatic,” Crowe says. “Maybe we upped it one degree. Whatever Joni says, I’m down with it. Because I’ve been around her when she’s not happy and there is no bullsh-t.”

“Len Berman and Michael Riedel in the Morning” airs weekdays on WOR radio 710.