What kind of clothing sale has DJs and performance artists as the stars? Or pairs designer fashions with hoodies and sneakers? Or offers piercings along with $4,850 Givenchy orange leather pants? Call it the millennial mashup.

Old-line department stores and fashion brands are rejiggering sales floors and websites to court millennials in their twenties and thirties and the even younger members of Generation Z. To woo this elusive demographic, department stores like Barneys New York and Nordstrom are concocting entertainment-filled Instagrammable shopping experiences with exclusive “drops” of limited-quantity products. They are hosting brief pop-up sales, merchandising high-end brands alongside casual ones and loading up on items that can be personalized and customized. Among their exemplars are Dover Street Market, Ssense, Maxfield and other specialty stores that have figured out what makes millennials tick—and shop.

Here’s how veteran retailers are taking a page from their cooler counterparts to captivate the next generation of shoppers:

Millennials defy uniforms but one fixture of their wardrobes is streetwear—hoodies, tees, sneakers and baseball caps often emblazoned with bold graphics, colors or logos. “Basically, streetwear is fashion today,” said Robert Burke, of luxury-goods consultancy Robert Burke Associates. Prices range widely, such as $155 for Nike Air Force high-top sneakers and $575 for a logo hoodie by the label Off-White.

But streetwear alone won’t draw younger consumers. Stores have to mix up the selection, offering high-fashion options, too. Traditional retailers’ practice of compartmentalizing brands and categories “is not appealing today,” to millennials and Generation Z, Mr. Burke said.

Dover Street Market, the avant-garde store created by the heads of label Comme des Garçons, was a pioneer in displaying streetwear labels alongside designer offerings. In its New York shop, which opened in 2013, streetwear brand Supreme was next to Prada. The approach reflects how younger consumers dress and made high-end designer fashion seem less intimidating to them.

Nordstrom took note. The Nordstrom Men’s store that opened in New York in April carries more streetwear and edgier fashion brands, said Paige Thomas, Nordstrom’s executive vice president and general merchandise manager for men’s apparel. To draw younger shoppers, she said, the store mixes brands at different prices and styles more than usual, “from Vans to Valentino and Nike to Balenciaga.”

To sustain its mix-it-up appeal, Dover Street Market departed from another retail tradition. “When we open a new store,” said general manager James Gilchrist, “we do our very best not to tell the brands who they’re next to so that they design the space they’re in without the knowledge of what’s going next to them.” Dover Street Market, which has stores in Tokyo, London, Singapore and Beijing, plans to open a Los Angeles outpost this year.

Specialty retailers are attracting young people by mounting temporary “pop-up” spaces and in-store events involving creative types such as artists, indie musicians and tattoo designers.

In recent years, Maxfield has run pop-ups that are both an art installation and a boutique for edgy or streetwear-inspired brands, including Off-White, READYMADE, Maison Margiela and Vetements. The pop-ups at the Los Angeles store often feature limited-edition exclusive products—in retail parlance, a “drop.” The events are popular with millennials, said Sarah Stewart, the buying director for Maxfield. “There’s a line outside waiting to get inside them,” she said. As word spread, the events “brought in a client that might not have known about us.”

“Millennials are the ‘experience generation,’ so pop-up and store events work well to draw their interest,” said Melanie Shreffler, senior director, insights, at research firm Cassandra. “They judge a good experience on its share-ability. For example, will they get some great photos for their Instagram to show off that they were a part of the cultural moment?

Last fall, Barneys New York joined with fashion blog Highsnobiety to host a weekend-long event aimed at millennials and Generation Z shoppers. Called “thedrop@barneys,” it featured exclusive, limited-edition merchandise and appearances by designers of streetwear and other brands such as Fear of God and Palm Angels, which are popular with millennials and Gen Z. Shoppers could get custom sneakers, tattoos and piercings. There were exclusive launches by Gucci and Alexander Wang, as well as by fashion-insider labels Ambush and Unravel Project. In its first day, the “drop” led to a 25% sales increase, with 20% of the customers new to Barneys. This weekend, the retailer will host a “drop” at its Beverly Hills store.

Jeff Carvalho, managing director of Highsnobiety, said that to attract younger shoppers, traditional department stores “are all pulling cues from those ‘indicator’ retailers”—meaning smaller, hip counterparts.

“Clienteling has to be rethought” by old department stores, Mr. Carvalho said. Such stores “have to cater to them differently if they want that youthful mindset to become clientele.”

Daniella Vitale, Barneys’ chief executive and president, said the concept came from a “company-wide effort for innovation” and acknowledged other influences.

While department stores traditionally hosted events for one individual, smaller boutiques often bring together several designers and artists. Dover Street Market periodically hosts a sprawling Open House that includes book signings, art installations, live music and sales of exclusive merchandise. The unique blend of attractions “really resonates with younger people,” Mr. Gilchrist said.

Ssense, a 15-year-old online retailer, scarcely promotes clothes on its site the way most mainstream retailers do. Instead, Ssense (pronounced essence) offers profiles of top musicians, artists, and recently, a chef. The site’s editor-in-chief founded the Berlin-based culture magazine 032c.

“Millennials don’t see distinctions between fashion, music, content and commerce,” said Krishna Nikhil, Ssense’s chief merchandising officer. The Montreal-based retailer, which opened its first bricks-and-mortar outpost there early in May, sells streetwear-leaning brands like A-COLD-WALL* alongside luxury labels like Givenchy. When a customer clicks on an item, it usually appears with merchandise from other brands, a departure from the retail playbook of showing a head-to-toe ensemble from one label. “That’s something young consumers in particular have connected with very strongly,” Mr. Nikhil said. About 80% of Ssense’s customers are between 18 and 34 years old, he said.

Bloomingdale’s has refreshed its web site to emphasize storytelling, adding curated content on trends and buzzy designer labels rather than merely filling the home page with merchandise. The goal is to create more engagement with consumers, especially younger ones.

“We have incorporated more editorial content created for the millennial customer,” said Frank Berman, Bloomingdale’s executive vice president and chief marketing officer. “In addition, we have been actively acquiring a younger consumer through advanced targeting on digital social platforms such as Instagram and curated influencer programs.”

“A key to understanding young retail consumers is to realize that many of them, especially Gen Zs, have been shopping online their whole lives,” said Ms. Shreffler, of Cassandra, the research firm. “While it may still seem revolutionary and simple to older consumers, young people are looking for this mature market to evolve and show them something new.”

Matthew Godin, a 22-year-old personal stylist in Toronto said Ssense is “the first place I check for anything.” He occasionally shops at Barneys but finds other department stores like Nordstrom and Saks staid. “Ssense has a really great mix of high-end, contemporary and emerging designers,” Mr. Godin said. “They also do a really great job at styling looks together in a really non-traditional way.”

Gian Rodriguez, a 17-year-old high-school student in Dublin, Ohio, said that aside from Supreme and Nike, he doesn’t “shop that much from other sites except Ssense.” He loves the range of brands and said the store appeals to members of his generation who are “starting to get into fashion and …need a reliable site” that understands what they want.