Nathaniel Rateliff and the Night Sweats recorded an episode for “Austin City Limits” on Sunday, Nov. 22. Photo by Scott Newton. Courtesy of KLRU-TV

There are those of us to whom a visit to the Stax Records museum in Memphis is like unto a pilgrimage to the Sistine Chapel. Those of us to whom the unvarnished and powerful horn-and-B-3-organ-propelled sound of Wilson Pickett, Sam & Dave, Carla Thomas and Otis Redding will sound ever and effortlessly cool and cutting edge. Those of us who regard “Knock On Wood” as a viable alternative to the national anthem.

For us, the accelerated rise to hip-dom of the Denver-based bar band Nathaniel Rateliff and the Night Sweats is akin to balm from Gilead. Rateliff & Co. have been burning up the concert trail and late-night talk show circuit behind the August release of their self-titled debut album (Rateliff has earlier releases as a solo artist). Sunday night they brought the show to ACL Live as part of “Austin City Limits” 41st season.

Fueled by a rocket-powered three-piece horn section, an afterburner of a B-3 organ and Rateliff’s own scorching tenor voice, the band rocked through a set that had the crowd head-bopping and hip-shaking from the first notes of their opening “I Need Never Get Old.”

Though Rateliff penned all the songs on the band’s latest album, their sound owes a debt to those who came before, particularly the artists of the Stax/Volt canon, the Band and the mid-period Van Morrison (listen to Rateliff’s “I’ve Been Failing” and Morrison’s “Youth of 1000 Summers” back to back and tell me I’m lyin’).

Those are all noble antecedents and the shadow of their influence detracts not at all from the Night Sweats’ crowd pleasers like “Loot It Here,” “Out On the Weekend,” “Mellow Out” and the foot-stomping, crowd-pleasing climax, “SOB.”

The band’s set wasn’t merely one long soul vamp. They mixed up the tempo with the eerie, jazzy “Shake,” the country flavored ”Wasting Time” and the aggressively rocking “Trying So Hard Not To Know.”

By way of a finale, the band returned for an encore while the crowd was still echoing the choral gospel chant of “SOB” and segued seamlessly into the Band’s “The Shape I’m In.” A nice tip of the hat and a nice way to cap a vibrant and exciting set.

After the show, in a bar across the street, some expatriate fans were recounting tales of seeing Rateliff and his cohorts gigging at local bars in Colorado and marveling at how far the band has come. It’s a great feeling to see the local boy make good.