A decade ago, they were New England Conservatory students playing an arty blend of jazz and country. Just a few years back, they could still be heard in small rooms like Club Passim and the Lizard Lounge. But everything’s changed for the members of Lake Street Dive.

First, a video of them singing a Jackson 5 cover on a Brighton sidewalk went viral. Then last September, T Bone Burnett tapped the band to join the likes of Patti Smith, Jack White and Marcus Mumford for a New York concert that aired on Showtime, celebrating the music of Inside Llewyn Davis. And with their February release, Bad Self Portraits, Lake Street Dive seized the national spotlight, hobnobbing with David Letterman and Stephen Colbert on late-night TV and finding themselves dubbed “The Year’s Best New Band” on the cover of Rolling Stone. This summer, the quartet has been rolling through major festivals, from Bonnaroo to Newport Folk, on the way to a Sept. 7 homecoming at Boston Calling on City Hall Plaza. As David Byrne once sang, how did I get here?

“If we were asked to repeat the last 10 years step by step and have the same results, I don’t know if that would be possible,” says trumpeter/guitarist Mike “McDuck” Olson, attributing his group’s seemingly overnight breakthrough to “good luck and happy accidents and falling ass-backward into success.”

“It did happen sort of quickly, and in a way that we didn’t realize was going to happen,” adds lead singer Rachael Price. “At the same time, we see it as the positive result of 10 years of hard work.” Those years included some lean times early on. “We didn’t always have nonstop gigs, and we weren’t able to support ourselves,” Price recalls. “But we were really good friends. We really enjoyed playing with one another. So if we’re in a bar with 10 people or in a sold-out 1,000-seater club, it doesn’t make that much difference.”

Upright bassist Bridget Kearney and drummer Mike Calabrese round out the tightknit foursome and contribute much of the songwriting. “There’s something that’s always going to be kind of exciting and attractive about a band that functions as four equal contributing members,” Price says. “That’s actually a little more rare than you’d think it would be. There’s no leader, no one star.”

Of course, as a frontwoman with a fetching, elastic alto who’s drawn comparisons to Ella Fitzgerald and Etta James, Price commands the most attention. Olson adds that he, Kearney and Calabrese faced more limited prospects as professional jazz bandleaders than Price did as a singer. On the other hand, he says, “The point of this band from the beginning was to be a band where if you switched out one member, it couldn’t be the band anymore. We aren’t interchangeable parts. We’re not Legos attached to the plastic bumps on Rachael’s back.”

Indeed, each member lends a signature element that’s only magnified on stage, from Kearney’s deftly slapped bass to Olson’s trumpet filigrees to Calabrese’s snappy backbeat, sometimes delivered with one hand on a shaker or a tambourine to his chest. Yet what likely most fuels Lake Street Dive’s success as a four-way entity are the tonally distinct vocal harmonies sprayed behind Price’s lead.

“Most of our rehearsing is spent doing background vocals,” Price says. “We’ve done songs for six years, and we’re still going back and saying, ‘Is that the right place for you and your voice? Would that sound better if you put it higher or if you were lower?’ We’re constantly examining them and making sure they’re punching and cooing in the right places.”

Sometimes they draw from pop and soul masters. “We definitely have reference songs that we call on,” she says. “We say, ‘Well, let’s listen to the background vocals on “Your Love Keeps Lifting Me Higher” ’ and take something like that. We take a lot from the Beatles because their stuff was so rich with harmonies.”

It’s a musical palette that’s evolved since Lake Street Dive’s founding. “Our stuff was a lot weirder. It was a little avant-garde,” Price says. But when band members compared notes, they realized the music they truly loved came from the classic pop and soul realm—Paul Simon, Sam Cooke and Motown. “It was us saying, ‘Hey, this is what I like listening to,’ and ‘Hey, what do you know, me too!’ ” Olson recalls. “ ‘Why are we playing this weird jazz bullshit? Why don’t we play songs like the Beatles? Why don’t we play songs like Otis Redding?’ ” The shift in sound suited their moniker. “We called ourselves Lake Street Dive because we wanted to be the kind of band that could play in a dive bar,” Price says of the name, coined after a bar-heavy street in Olson’s Minneapolis hometown.

Soon the band moved from a focus on recast covers (including George Michael’s “Faith,” Hall & Oates’ “Rich Girl” and the Jackson 5’s “I Want You Back” on its 2012 EP Fun Machine) to shaping clean, retro-styled originals. The resulting Bad Self Portraits delivers sophisticated simplicity. Price coyly rides the doo-wop teases of the Kearney-penned title track—about a lonely woman with no one else to photograph—before the group erupts in wide-screen harmonies for “Stop Your Crying.” The brisk “Bobby Tanqueray” lends a frisky ’50s rock edge, while the soulful, swinging raveup “You Go Down Smooth” soars as the standout track.

The band recorded the album in late 2012 with Josh Ritter’s keyboardist/producer Sam Kassirer at his Maine farmhouse studio, the Great North Sound Society. Ironically, it was during their time at that remote location that the video of their sidewalk take on “I Want You Back” exploded online. Someone shared it on Reddit and—in a surreal twist on six degrees of separation—even actor Kevin Bacon tweeted his love.

“We didn’t have cellphone service or anything. And we checked the views on that video, and it had gone completely viral,” Price says. “We were like, ‘What’s going on?!’ ” Much of the appeal of that video, filmed by their friend Greg Liszt (banjo ace for Crooked Still and the Deadly Gentlemen), comes from its stripped-down performance. The group vocalized around a single microphone, with Calabrese playing just a snare drum and cymbal alongside acoustic bass and trumpet.

“We refuse to rely on a lot of production to make a song,” Olson says. “It’s got to work with the barest of musical elements, because if that works, we can do essentially anything to it—and it’ll be icing on the cake.”

Lake Street Dive took a similarly intimate guerilla approach to its stunning rendition of “You Go Down Smooth” during September’s Inside Llewyn Davis show at New York’s Town Hall. “We were gaga at all the other musicians backstage,” Olson says of what was an eye-opening experience for everyone, including national press like Rolling Stone and television talent bookers. “We left and told our friends, ‘Oh, we met Elvis Costello, we met Joan Baez, oh my God.’ It didn’t occur to us until much later that there was an audience.… There were all these industry folks there. I’m actually kind of glad that we didn’t realize!”

Since that Jackson 5 cover (now past two million hits) went viral, the band’s profile has only grown on YouTube, where college a cappella groups have covered “You Go Down Smooth.” Even a 1998 performance of a 12-year-old Price singing in Spain with her father’s choir has drawn more than 65,000 views.

“It’s kind of magical the way it’s running now,” Olson says. “I worry for the future if things become super economy-driven with the Internet and YouTube. This is something we’ve been thinking about and talking about a lot lately in the band, where everyone can post anything right now, which is truly a beautiful thing.”

Everything has certainly clicked for Lake Street Dive, even with the release of Bad Self Portraits delayed because of a contract dispute with an investor for Price’s prior venture as a jazz singer. “Fortunately, we got it worked out,” she says. “It kinda ended up being positive in the end, because the year that we couldn’t release the album, all we could do was tour nonstop. And it built our fan base in a way that once we could release the album, we were in a completely amazing place.”

It’s a long way from early rehearsals that felt more like parties (“There were a lot of chips being eaten,” Olson says) and gigs in bars as tiny as Toad in Porter Square. Now the quartet is working new originals into its concerts and on course to make another album by early next year, amid greater expectations—and greater confidence.

“I’d be lying if I said we were immune to the pressure of the sophomore album, but we’re trying not to think about that,” says Olson, who still lives in Jamaica Plain, though his bandmates have relocated to New York. “We may have jazz roots and a healthy appreciation for various art musics, but nowadays we’re concerned with things far more base than we were in the beginning. We just want to write hooks, man, and have people dance to the backbeat and go home singing the chorus. Not because it’s a strictly commercial venture, but because that’s what we want as music fans. We want to go to a show and remember the tunes.”