Cuban-born percussionist, songwriter and vocalist Pedrito Martinez made his latest appearance at the Kennedy Center on Saturday. (Danielle Moir)

It’s not instantly clear that there’s jazz in Havana native Pedrito Martinez’s music. The percussionist leans toward a pop take on Cuban mambo, more focused on song form and sustained rhythmic momentum than on improvisation. (Although, in fairness, the latter isn’t absent.) Slowly, however, his quartet brought a Saturday-night Kennedy Center audience around to its way of doing things.

Opening with a simmering groove led by Martinez’s congas and Yunior Terry’s bass, a substitute for regular bassist Alvaro Benavides, the group quickly exploded into a four-part vocal with a straight mambo feel, down to pianist Edgar Pantoja-Aleman’s guajeo riffs. It took a minute to realize that it had a 12-bar blues structure. Then came what at first sounded like a slow jam but was a long, mid-tempo song with more harmonized vocals. The rhythm was so infectious that Martinez stood up in the middle of his conga solo to gyrate his hips.

The audience at the KC Jazz Club may have known what it was in for; Martinez has played there before. But while people were clearly enjoying themselves, they were sitting politely and clapping in all the right places — a run-of-the-mill jazz crowd.

Martinez wasn’t having it. I saw the quartet a year ago in the Dominican Republic, where they played to sellout local (and dancing) crowds for whom these Afro-Caribbean rhythms were second nature. The band treated the Kennedy Center crowd precisely the same, even giving shouts and yips in Spanish during the instrumental interludes.

When that didn’t rouse them, Martinez took the microphone before a tune to say: “For this next song, pay attention. Wake up. It’s Saturday.”

But it took until the fifth and penultimate tune for spectators, or at least their feet, to get the message. As the funky beat commenced, Martinez and second percussionist Jhair Sala noticed some people tentatively rising from their seats. “Come on,” they coaxed. “Don’t be shy. Get up!” They did — and so did a hefty portion of the room, soon dancing with abandon. Those who didn’t dance clapped and whooped from their seats. One savvy spectator beat out the standard Afro-Latin clave pattern against a thumping Terry solo. A concert had finally turned into a party.