Drummer Matt McAllister, tenor saxophonist Josh Kline and bassist Jon Massey of Animal Mother. (Patrick Smith)

The key moment of Sunday night’s set by Animal Mother, a self-styled “garage jazz” trio from Cincinnati, came near the end of their set when they suddenly turned out Duke Ellington’s “Solitude.” It was closer to mid-tempo than the song usually gets, just a beat or two faster than Billie Holiday’s studio recording, and contained a bluesy aspect that was absent from the rest of the show — especially when tenor saxophonist Josh Kline traded fours with drummer and leader Matt McAllister as the song was wrapping up.

It was the key moment not because it was any better than the remainder of Animal Mother’s set; it wasn’t. But the band had spent most of the evening at Twins Jazz pulling well away from jazz convention. Their energy and aesthetic had more in common with punk or post-rock (hence the term “garage jazz”). “Solitude,” however, suggested that these guys — unlike many declared jazz musicians — had mastered the music’s basic foundation before reimagining it.

And that reimagination was pretty thorough. The first 20 minutes or so, McAllister announced at the start, would feature covers of “our favorite jazz tunes.” That included three numbers; this writer didn’t recognize any of them. Animal Mother completely suffused them with a unique energy. The second tune, for example, had echoes of Ornette Coleman, but hit peak after peak, like ocean waves at high tide. That energy actually got the better of Kline on the next selection: He pushed the tempo until he was out at the head of the beat, forcing McAllister and bassist Jon Massey to rein him back in.

As much adrenaline as Kline had, though, McAllister was unquestionably the engine that drove the band. One could hear it in the 10 original tunes, all of which (save one) were his.

The theme to “Power Dance,” in fact, had Kline essentially doubling the drum line. When the saxophonist started improvising, he and Massey were harmonically in synch but had different rhythmic conversations. It was up to McAllister to thread the needle — and he did, with a rock backbeat that nonetheless grooved hard.

Meanwhile, “Floats on My Pillow” featured the bassist (easily the trio’s most melodic player) in a dreamy, complex solo that might have crossed over into soporific had the drummer not been slowly coming to a boil, with a thrash and attitude that suggested Keith Moon gone jazz, and bringing Kline with him.

The audience at Twins was light, partly an occupational hazard of Sunday nights. Still, Animal Mother deserves more ears, not least because they slyly suggest that they have even more musical ingredients than meet the ear. For example, two of their songs, “Floats on My Pillow” and “I Can Hear the Soft Breathing,” both quote the lyrics of the same Simon and Garfunkel song.