By NATE CHINEN

Groove has always been an essential element for the jazz guitarist John Scofield, expressing itself in ways either subtle or obvious, depending on the setting. “Piety Street” (Emarcy), released last week, falls in the obvious category, with a fortunate twist: it’s Mr. Scofield’s old-time gospel album, recorded in New Orleans with a band drawn mainly from that city’s robust R&B scene. It’s a basic concept, and it makes all kinds of sense.

The same could be said of Mr. Scofield’s staunchly exuberant show at B. B. King Blues Club & Grill on Sunday night. Joined by the core players from the album — the pianist Jon Cleary, the bassist George Porter Jr. and the drummer Ricky Fataar — he played the greater share of its songs, achieving the proper blend of grace and grit. He didn’t sound like a visitor in the realm. He sounded at home and happy to be there.

And crucially, he seemed aware of both the music’s needs and its potential limitations. Instead of navigating fast-moving streams of rhythm and harmony, as in his post-bop bands, he was leaning on a stable firmament. So he dug in deep, often parceling his notes into flinty riffs. When he did let loose with a digressive chord or a ribbon of arpeggios, it was usually in the heat of full-group catharsis.

The band brought depth and shading to even the most straightforward rhythmic conceit. Much of this was the work of Mr. Porter, known as a member of the Meters, the epochal New Orleans funk band. A canny embellisher, he often created a counterpoint to Mr. Scofield’s leads.

He also sang, notably on “Never Turn Back,” a Thomas A. Dorsey tune that in this version became a sprawling but hard-driving jam.

Chief vocal duties fell to Mr. Cleary, who has an appealingly weathered voice and a smartly soulful attack. (On the album he sometimes yields the floor to John Boutté, a more incandescent singer, but that missing substitution barely registered here.)

In a few songs, including “Something’s Got a Hold on Me,” Mr. Cleary got vocal backing from one or more of his band mates, suggesting the vintage style of a group like the Dixie Hummingbirds. His keyboard playing, on a pair of synthesizers set to evoke a piano and a Hammond B-3 organ, was rollicking and pithy.

Mr. Scofield reinvented some of the songs in the repertory, outfitting “Motherless Child” with sharp new harmonies and bestowing a Celtic tinge on Hank Williams’s “Angel of Death.” But the more satisfying moments were the simplest. “It’s a Big Army,” the set closer, plowed straight into rafters-raising territory, and Mr. Scofield responded with a frolicsome surrender.