One summer night in 2019, Alana Haim was jet-lagged, tossing and turning in a London hotel bed, when her phone pinged with an email from the acclaimed filmmaker Paul Thomas Anderson.

This was not particularly out of the ordinary: Anderson had become a close friend of the family in the years since he’d started directing music videos for Haim, the Grammy-nominated rock band Alana is in with her two older sisters, Este and Danielle. (Their mother, Donna, was also Anderson’s beloved elementary-school art teacher — a fortuitous coincidence he realized only after having already met her daughters.) When the band is on the road, Anderson will occasionally send the Haim siblings affable emails: a silly YouTube video, an article that might inspire them. But this message was different, and a little mysterious: Just an untitled Word document.

“All of a sudden, a script opens up,” Haim said over a video call from her home in Los Angeles,

“And the first name on the script is Alana.” Save for a few appearances playing herself in music videos, Haim had never acted before, and this was the first movie script she’d ever read. “It was like ‘EXTERIOR,’” she recalled, giddily. “I was like, here we go. We’re reading a script. This is the movies.”

As she read the screenplay for what would become “Licorice Pizza,” Anderson’s warm and nostalgic ninth feature, Haim thought he had sent it to let her know he had named a character after her. “I was honestly just flattered that he was using my name,” she said. “Because when you think about Paul Thomas Anderson movies, the names are so incredibly iconic,” she said, citing the porn star Dirk Diggler of “Boogie Nights” (1997) and Reynolds Woodcock, the tempestuous fashion designer that Daniel Day-Lewis portrayed in “Phantom Thread” (2017). “I mean, I like my name, but do I think my name is iconic? Not when you put it next to, like, Reynolds Woodcock. But I was flattered. I was like, ‘Paul’s going to use my name in a movie.’”

When presented with Alana’s version of events over the phone later that same day, Anderson sighed and then laughed for a long time. “Wouldn’t it have been completely rude and insane of me to send her a script with a character named Alana, only to say, ‘Thanks for reading it, I appreciate your notes, I’m going to go hire an actress to play a woman named Alana? Oh and by the way, she has two sisters named Este and Danielle and there are multiple situations that have come from your life.’ What kind of friend would I be? That’s terrible.”

But that would have been about as plausible as what was actually happening: A famous auteur was asking Haim, who had never been in a movie before, to carry his next feature. Later that night when they spoke on the phone and Anderson clarified his request, Haim — in a torrent of “word-vomit” — said yes immediately. A few hours later, the first doubts set in: “What if I’m just terrible? I was like, ‘I don’t even know where to look. What if I look at the camera?’”

Miraculously, she pulled it off in spades. “Licorice Pizza” establishes Haim as a revelatory and magnetic screen presence, a unique amalgamation of daffy, Carole Lombard screwball, early Sissy Spacek fresh-faced guilelessness, and an offbeat cartoon character’s nervy, can-do energy. Even when she’s sharing the frame with Sean Penn, Tom Waits or Bradley Cooper, it is her face — freckled, elastic, unpredictable — that commands the viewer’s attention. Critics have raved about the performance; David Rooney of The Hollywood Reporter called it “one of the most exciting screen debuts in recent memory.”

Anderson said he knew Haim would be good but “I didn’t know she was going to be that good. I’ve worked with the same guys for like 20 years, and I just kept looking around at them for verification. Like, you have to tap me on my shoulder to make sure I’m seeing what I’m seeing. Don’t let me be delusional. And everybody collectively on set was seeing what I was seeing — her skill and the way you can photograph her.”

It helped that her co-star, the effortlessly charismatic Cooper Hoffman (son of Philip Seymour Hoffman, who was a frequent Anderson collaborator) had also never been in a movie before. Anderson cast him late in the process, after auditioning a number of young actors who felt too mannered and formally trained to match Haim’s naturalistic style. Hoffman and Haim had met briefly through Anderson five years prior, never thinking their paths would cross again, but as soon as they read together, Haim recalled, “It was like, oh, we’re a team. We can take on the world together.”

Despite the characters’ relatively chaste relationship, the age gap between them has caused some controversy. In real life, Haim, who turns 30 this month, is 12 years older than Hoffman (they bonded so much during the shoot that she still calls him “one of my best friends”), though in the movie her age is a little ambiguous. At one point the character says she’s 25, but there’s a pause between the two numerals that suggests she might be rounding up. “There was never really a conversation between me and Paul about how old Alana was,” she said. “Somewhere in her early 20s. I say some ages in the movie, but you don’t really believe Alana. She kind of doesn’t even know how old she really is? She’s very secretive. But really, it’s about her and Gary’s friendship more than anything.”

When we spoke on a late November afternoon, Haim was battling a sinus infection she blamed on the Santa Ana winds. As a Southern California breeze tickled the curtains of her open living-room window, she occasionally paused our conversation to blow her nose with humorous theatricality. (“Oh, that was a lot!”) She wore a white T-shirt, jeans and, around her neck, her most prized possession, a “Sisters of the Moon” pendant given to her by one of her idols, Stevie Nicks. In conversation Haim is garrulous and ebullient, occasionally clipping the ends off her sentences in an excited hurry to get to the next thought.

As they were shooting, Anderson found that the actor Haim most reminded him of was Joaquin Phoenix, whom Anderson directed in “The Master” (2012) and “Inherent Vice” (2014).

“She can throw herself into something, a lot like Joaquin,” Anderson said. “You cannot tell if they’re completely out of control, or if they’re so in their body that they’re able to make it look like they’re out of control. They’re very similar. It’s weird. They’re both feral, you know? You’re not really sure what’s coming next.”

Her years onstage playing guitar, keyboards and percussion certainly taught her how to ground herself amid the chaos of a film set. “Being in Haim, I’m doing so many different things and there are so many different distractions that you have to tune everything out and just be very present in your body,” she said. “And I think that really helps with shooting a movie.”

Seeing herself in close-up on a huge screen for the first time was, she admitted, a bit uncomfortable: “Look, for my future boyfriends that I’ll maybe have, would I love to see less acne and maybe more glamorous vibes?” Haim asked rhetorically. “Of course. But it wouldn’t be truthful to the movie. Because growing up in the Valley where it’s 100 degrees outside, you would look worse if you wore makeup, because it would melt off and you’d look insane.”

But those supposed imperfections — and her contagious brand of self-acceptance — are at the core of Haim’s refreshing onscreen charm. “I feel like there’s this whole thing where everybody has to be perfect in all these movies,” she said, candidly admitting that the only reason her skin looked “impeccable and lovely” on our call that day was because she was using a Zoom filter. “But, I have acne, and there’s nothing I can do about it — and that’s OK!”

Raised in the San Fernando Valley, the Haim siblings all took up instruments at a young age and formed a family band. What they lacked in social capital, they made up for with sisterly camaraderie and humor. “We all wanted to be Barbra Streisand in ‘Funny Girl,’” Haim said. “That was our Bible growing up. Like, ‘Oh, we might not be the most gorgeous person in the seventh grade, and no one wants to make out with us, but we could be the funniest!’”

The sisters had their first gig as a trio when Alana was just 10, at Los Angeles’s storied Jewish institution Canter’s Deli. Their breakthrough came in 2013 when they released their debut album, “Days Are Gone,” a collection of sleek, percussive pop-rock songs. They’ve since collaborated several times with their former tour-mate Taylor Swift, and their best and most recent album, “Women in Music, Pt. III” (2020), was nominated for the album of the year Grammy.

Even though the siblings all harmonize and trade instruments, Alana is still known in the band, as in the family, as “Baby Haim.” Danielle is the de facto lead singer and guitarist, while the bassist Este is known for the gloriously over-the-top “bass faces” she makes onstage. Alana sometimes falls through the cracks. “I’m the baby, so that’s how I grew up with my siblings: ‘I’m just happy that you guys want me to hang out,’” she said modestly. “That was my whole upbringing.”

All the members of the Haim family appear sporadically in “Licorice Pizza” — their father, Mordechai, is a bona fide scene-stealer. But Alana is the movie’s beating heart, and her star turn feels like her long-delayed “Funny Girl” moment. That was apparent from her very first day of shooting: she was not only driving a vintage moving truck that required her to learn to operate a stick shift, but also improvising hilariously alongside a deliriously entertaining Bradley Cooper, who plays a manic version of Streisand’s onetime boyfriend, the producer Jon Peters. “At the end of the day, once I got the hang of it, I felt like a badass,” she said. “I was like, not only can I drive stick — but a ’70s U-Haul with a movie star and my best friend in the truck.”

She’d love to keep acting — and working with Anderson — if the right projects arise, but she’s also happy to have a day job to fall back on. “After this chapter is over with ‘Licorice Pizza,’ I go back on tour with my band, and I’m back to my other job that I love so much,” she said.