Listening to Alabama Shakes’s just-out debut album, “Boys & Girls,” you can hear the echoes of their years as a cover band in the way the record easily straddles classic rock, blues, country and soul. Not long ago, when they used to play for gas money, they did songs by the titans of classic-rock radio:The Stones. Zeppelin. Creedence. Sabbath.

But during a sold-out headlining set at Baltimore’s Rams Head Live on Saturday night, the material was their own. Shakes numbers such as “Hold On” and “You Ain’t Alone” might be younger than Siri, but they have the consoling authority of standards. While the songs sound more like 1972 than 2012, the sight of an African American woman fronting a band of white dudes remains uncommon. Indeed, the only song Shakes singer Brittany Howard introduced at any length — the new album’s title track — is all about how antiquated social norms can threaten relationships we treasure. Howard has one of those nimble-yet-powerful rock-soul voices like Tina Turner’s. You can imagine her commanding rooms bigger than Ram’s Head for decades to come.

The band’s playing sat comfortably in that Next Big Thing sweet spot: disciplined enough to show they’ve put in the time, but loose enough to show every gig still matters. Eschewing shapeless, energy-sapping jams, they kept the focus squarely on the songs. They had the confidence to open with their quietest tune, the brief “Goin’ to the Party,” before lighting into “Hold On,” their slow-burning lead single. As the hour got later the tempos got faster: The Chuck Berry-esque “Heavy Chevy” worked the crowd into a sweaty froth, and the encore’s one-two punch of “On Your Way” and “I Ain’t the Same” managed to give a show that clocked in at only 70 minutes a finale worthy of an epic.

Klimek is a freelance writer.