They all studied at Boston’s prestigious New England Conservatory of Music and put in a decade establishing themselves as serious musicians. So you can imagine how surprised the members of Lake Street Dive were when, of all things, a whimsical YouTube video of them street-busking with a Jackson 5 song launched their career to the next level.

“We can thank a million people with desk jobs who suddenly shared our video instead of doing their work,” cracked Mike Olson, the St. Louis Park-reared guitarist/trumpeter who gave the jazzy buzz band its Minneapolitan name.

“We’re certainly not complaining about that,” he added.

Indeed, Olson and his crew are thanking their lucky stars, given what has transpired since the “I Want You Back” video went viral last year. The quartet was hand-picked by T Bone Burnett to perform at a promotional concert in New York for the Coen brothers’ movie “Inside Llewyn Davis,” an all-star affair that became a TV special for Showtime. More small-screen exposure came via David Letterman and Stephen Colbert. NPR has been hyping the band, too.

The buzz helped push Lake Street Dive to No. 18 in Billboard last week with first-week sales of its third studio album, “Bad Self Portraits.” A collection of warm, playful original tunes anchored by stand-up bass and minimal electric instrumentation, the record was praised by Rolling Stone for its “Motown-meets-Muscle Shoals soul nostalgia [and] flashbacks of Amy Winehouse” — the latter a nod to the group’s hard-bellowing lead singer, Rachael Price.

On the local front, “A Prairie Home Companion” was hip to Lake Street Dive early on, featuring them twice in 2012. Following an intimate show at Icehouse in August, the quartet quickly sold out the Cedar for Olson’s homecoming gig Saturday.

“It’s definitely a huge personal thrill for me getting the attention there in Minnesota,” he said, singling out the coincidental support from Garrison Keillor and fellow St. Louis Park natives Joel and Ethan Coen — “heroes of mine.”

After graduating from Blake High School in 2001, Olson put in two years at the University of Wisconsin-Eau Claire before enrolling at the New England Conservatory, where he met the rest of the group. He returned to town often to visit his parents, which inspired the band name.

“The idea was to evoke the typical, everyday American dive bar, and not one particular dive bar,” Olson said, citing the not-so-divey Bryant-Lake Bowl as his go-to Minneapolis hang.

“I’m proud it’s a Minnesota thing, but it’s not the best band name, in hindsight. People are always getting it wrong, like ‘Lake Street Drive.’ ”

People took a while to catch onto Lake Street Dive in general. The members have been playing together since 2004. In that time, Olson recounted, “We fell under the wing of Boston’s Americana scene, and then for a while we were taken in by the bluegrass community. And when we hit the road more over the past couple years, we fell in with the jam band scene, which was great to us.”

All of which is to say, Olson gladly admitted, “We don’t easily fit into any category.” Price had also made a name for herself in Boston as a solo jazz singer, which partly explains how the band came to play the Jackson 5 and many other seemingly random cover songs (including tunes by George Michael, Hall & Oates and the Drifters).

The group is rounded out by another woman and man, bassist Bridget Kearney and drummer Mike Calabrese.