Before the women became fashion designer and muse, they connected over relationships of a different sort.

“We would talk about cute boys,” Christian Joy said of her early conversations with a young Karen Orzolek, the frontwoman of the rock band the Yeah Yeah Yeahs, who is now known simply as Karen O.

This weekend, the Yeah Yeah Yeahs are scheduled to play in Mexico as part of the band’s tour for its fifth and latest album, “Cool It Down,” which was nominated for two Grammy Awards this week. Karen O plans to perform in one of the newest costumes that Ms. Joy made for her: a multicolored studded jumpsuit complete with red tinseled opera gloves and a glittering red, black and blue cape featuring a sunburst.

“I wanted her to take it to a really grandiose place,” Karen O said in a phone call, noting the look was inspired by the occult films of the British director Ken Russell, mysticism and ’70s glam rock.

The costume, which Karen O debuted last month at a concert at Forest Hills Stadium in Queens, is among the most recent outfits born of her creative partnership with Ms. Joy. (Another: a kaleidoscopic bodysuit trimmed in primary-colored tape.) Both “very tomboyish” women, as Karen O put it, who favor D.I.Y. over runway fashion, the designer and muse have put their own theatrical stamp on rock-star style since they started working together 21 years ago. “I think a lot of people don’t realize that we were doing this stuff before Lady Gaga,” Karen O said. “I’m sure she was seeing some of this stuff, too.”

Katie Baron, the author of “Fashion + Music: Fashion Creatives Shaping Pop Culture,” compared Karen O’s partnership with Ms. Joy to that of David Bowie and Kansai Yamamoto, the fashion designer who made many of Bowie’s costumes.

“There were tons of mini Karen Os at Yeah Yeah Yeahs shows,” said the author Lizzy Goodman, whose book chronicling New York’s 2000s indie rock scene, “Meet Me in the Bathroom,” was the basis for a new documentary. “You would see tattered prom dresses, fingerless gloves, fishnets. They radiated and reflected what we were all feeling about how we wanted to look and have permission to dress.”

Ms. Joy, 48, met Karen O, 43, in 2000. At the time Ms. Joy was working for Daryl K, the cult fashion brand known for its low-rise flare jeans, at its now-closed store in the East Village. Karen O, then an aspiring singer and film student at N.Y.U., would often stop by.

Born Christiane Joy Hultquist in Marion, Iowa, Ms. Joy was then experimenting with fashion design using castoff prom dresses bought at a Salvation Army store near where she was living in the Clinton Hill neighborhood of Brooklyn. She taught herself how to deconstruct the dresses, which she would then refashion into new garments and sell at Timtoum, a boutique on the Lower East Side that is also now closed.

She and Karen O quickly became friends, discussing musicians that both liked (Beck, Sparklehorse) and films that Karen O made at college. One film in particular struck a chord with Ms. Joy: “Nice Mice in a Cruel World,” about a group of rodents brutally murdered by marauding cats. “I thought, ‘This girl is insane,’” Ms. Joy recalled. She added, “To me art and fashion were this higher thing. I didn’t realize that you could be funny and ridiculous. That sent me into this whole other place.”

Soon after, Karen O gave Ms. Joy a CD featuring the band she had just formed with Brian Chase and Nick Zinner, called Yeah Yeah Yeahs. “I thought, Ugh, this is going to be terrible,” Ms. Joy recalled. Then she listened to the music. “I remember hearing it and thinking, ‘Holy crap, this is really good.’” In 2001, Karen O asked Ms. Joy to design a dress for the singer to wear at a February show by the band at The Cooler, a nightclub in Manhattan’s meatpacking district.

“I had one night to make it,” said Ms. Joy, who began by taking a secondhand blue-satin prom gown and shredding it. She then added plastic flowers to the drop-waist dress, which looked as if it had been sent through a wood chipper, and wrote “Yeah Yeah Yeahs” on it with white paint. “It was hideous,” Ms. Joy added, laughing.

Karen O remembered the dress differently: “It was just explosive to the eye,” she said. “I thought, ‘Dear Lord, let me be able to live up to this dress onstage.’”

As the band’s profile rose, so did the number of Karen O’s (often last-minute) requests for outfits designed by Ms. Joy. “Karen would call and say, ‘Hey can you make me something, we are getting shot for Rolling Stone tomorrow,’” Ms. Joy said.

The singer’s early costumes made by Ms. Joy — another reworked prom dress covered in fake dollar bills for a 2003 feature in The Face magazine; a blue spandex leotard with silver peplum that the singer wore on a 2004 cover of Spin — differed in style from what the Strokes, Interpol and other rock acts at the time were wearing, Karen O said.

“The look that everybody was sporting was just like striped shirts, skinny jeans, leather jackets or Member’s Only jackets,” added Karen O, who in the music video for the Yeah Yeah Yeahs’s 2009 song “Heads Will Roll” wore a red spandex tank dress with poufy leg-of-mutton sleeves that Ms. Joy made using a shower curtain she had bought at a dollar store.

Designing more pieces for Karen O required Ms. Joy, who briefly studied photography at Columbia College Chicago before dropping out, to learn how to use a sewing machine and the art of pattern making. To this day, she has had no formal training in fashion design. Since 2003, Ms. Joy has worked from a studio at her home in the Greenpoint neighborhood of Brooklyn, which she shares with her husband Jason Grisell, a musician. She has one assistant who has worked with her for 18 years; otherwise, the Christian Joy atelier is a maison of one.

Raised with five siblings, Ms. Joy said that her mother, Connie Hultquist, who died last year, “really taught me how to survive on not a lot, how to work with not a lot, to persevere.”

Her collaborative process with Karen O hasn’t changed much over the years, though it has involved less face-to-face conversations since the singer moved from New York to Los Angeles in 2014.

Karen O will ask Ms. Joy to design something for a performance or video, occasionally providing scant references. There are no mood boards, no endless fittings. But there is “a sadomasochistic aspect of both our personal and working relationships,” Karen O said, explaining that Ms. Joy “tortures herself to come up with some brilliant idea, cursing my name every step of the way,” only for the tables to turn when the singer debuts an outfit onstage. The reveal, Karen O added, is “a bit of torture for me.”

Their partnership is rooted in “a deep trust,” Karen O said. “Whatever it is going to be is a million times better that anything I could guide her toward.”

“It doesn’t always work out,” she added. “Sometimes it’s a miss!”

One such miss the two agree on: a dress Ms. Joy made for Karen O to wear at a 2006 show at the Bowery Ballroom. It had “these really phallic striped stuffed appendages coming out of the neck,” Karen O recalled, and “pukey, fluorescent green spots” painted on it. (The dots, Ms. Joy said, were inspired by the artist Yayoi Kusama.)

The dress “was a masterpiece of being so bad it was good,” added Karen O, who wore it later that year for a feature in the French fashion magazine Self Service.

The Yeah Yeah Yeahs’s “Cool It Down” tour was the first time that Karen O commissioned pieces from another designer, Yuima Nakazato in Tokyo, who made the singer a holographic bodysuit, cape and hat that she has worn at recent shows. Ms. Joy has also designed clothes for other singers, including Brittany Howard of the Alabama Shakes and Maggie Rogers, between projects for Karen O.

But occasionally straying from their partnership has not diluted the strength of their sartorial bond.

“She’s got this gift to create happiness,” Karen O said about Ms. Joy. “What I wear onstage and how I present myself brings a lot of joy. That’s at the heart of it. It’s not about a trend. It’s just the joy of creating.”