Except for maybe the actual Replacements, the Dakota found the best possible hometown replacement for its two postponed shows this week.

Filling in for ailing Texas twang-folk vet Nanci Griffith, Gary Louris made his debut at Minneapolis’ downtown jazz haven on short notice Monday but acted as if he were an old acquaintance of the venue. He optimized its intimate listening-room qualities, choosing lesser-known fare over surefire crowd-pleasers by his beloved band, the Jayhawks.

Monday’s show also happened to be Louris’ first hometown gig since canceling a solo tour in the fall to undergo treatment for chemical dependency, about which he opened up early in the unusual yet unendingly satisfying two-hour set.

“I shipped out for a while; had a little problem with my usage,” he told the crowd, adding cheerfully, “but I’m back and feel great. So drink up!”

Monday’s set list was quite an intoxicating cocktail. Louris, 58, started with “True Blue” and other tunes from his 2008 solo album “Vagabonds,” even including “Three Too Many” and other outtakes from it. “As if the record itself isn’t obscure enough, I’m playing the B-sides,” he joked, although they proved lively additions, with opening act Kevin Bowe & the Okemah Prophets serving as his backers.

From there, Louris offered an overview of his non-Jayhawks work, including Golden Smog tunes (“Jennifer Save Me,” “Gone”) and tracks he co-wrote with the Dixie Chicks (“Everybody Knows”) and Nickel Creek (“Jealous of the Moon”).

Just when it seemed as if the Jayhawks would be mostly forsaken, three-fifths of the Jayhawks lineup appeared, starting with pianist Karen Grotberg for a lovely “Smile,” followed by drummer Tim O’Reagan and bassist Marc Perlman. The old gang stuck mainly to mid-era tunes such as “Trouble,” “One Man’s Problem,” “Save It For a Rainy Day” and “Better Days” — all songs rife with optimism, and thus especially well-chosen for the occasion.

For the encore, Chan Poling of the Suburbs provided the sole accompaniment on piano for a heart-mashing cover of Badfinger’s “Without You,” just one of many in the set that never would have gone over as well at a packed First Avenue as it did at the intimate Dakota.

See Louris’s full set list at startribune.com/artcetera