For a moment, forget that it’s been packing arenas for more than a decade, and consider the improbability of the Dave Matthews Band.

Formed in grunge’s early-’90s heyday, a time when nary a man could step on stage without an ax to grind and a guitar to smash, the Charlottesville-bred group propelled itself into the popular consciousness not with a blast of feedback but the gentle hum of an alto saxophone. The drummer mostly plays fills, rather than steady rhythms. The solos come courtesy of an electric fiddle player. The songs on its best-loved record, “Under the Table and Dreaming,” are the sum of eternally uncool elements — light jazz, progressive rock and a dash of new-age stardust. And yet, the band’s “fire dancer” bumper stickers adorn a lot of the hatchbacks you cruise by on the highway. The group has pioneered a funkier take on Americana and supplanted the Grateful Dead as the nation’s go-to ensemble for extended mellow and groovy improvisation.

On Saturday night the band brought its strange soft-rock brew to Jiffy Lube Live, performing a three-hour set that was evenly split between the oldest of the crowd’s old favorites and brand-new material.

Weary of the neo-hippie bracket, Matthews, the group’s principal songwriter, and his band mates spent most of the early ’00s courting a crossover hit; recording two albums, “Everyday” and “Stand Up,” that dialed back the group’s jammier impulses and seemingly sought artistic maturity via serious study of the Sting playbook.

But more recently, the quartet seems to have come to peace with its younger, looser self. The unreleased songs they played were staid and moody but sprawling. And the rest of the set was weighted with material drawn from the band’s debut, including extended versions of standbys such as “Warehouse,” “Satellite” and a 15-minute take on “Jimi Thing,” perhaps the least psychedelic song ever to be written about smoking pot.

In this, the Dave Matthews Band parts ways with its jam-band peers. The group solos and carries on at length, but the members generally steer clear of abstract zone-outs. Their crowd is short on tie-dye and black lights, heavy on boat shoes and madras shorts.

Another distinction that separates the group from its brethren: Dave Matthews is not afraid to be bummed out. Phish front man Trey Anastasio regularly sings about everything from feet, to worms, to weighing severed heads. Matthews spends a lot of time battling self-doubt. As a result, the Saturday set sometimes had an awkward rhythm, with the band building up steam only to burst the bubble with solemn and stripped fare.