Instead of making his sound a static thing, Mr. Haynes was flickering: working for the benefit of the music as well as the benefit of the show, even when laying back or making no sound at all. Several times he got up from his stool, prowled around the kit, shaking his shoulders and legs, and clicked his sticks together, or whacked a floor tom, or hit the edge of the cymbal at the start of a new chorus. Once he made the band sink into a period of silence and reanimated it with something like a kick-drum heartbeat. Once he got up in Mr. Garrett’s face and twirled a stick. Once, absorbing the feeling of a tune at his own speed after the rest of the band had started it, Mr. Haynes waggled the stick in his right hand, playing the air for a minute, like a draftsman preparing to sketch. And then he leaned into his ride cymbal and started again.

Image Roy Haynes, right, performing with from left to right, Danilo Perez, Wynton Marsalis, Kenny Garrett, and Dave Holland during “An Evening With Roy Haynes” at the Rose Theater at Lincoln Center on Saturday. Credit... Brian Harkin for The New York Times

The Fountain of Youth Band — it has gone through several iterations over the past decade — now has the saxophonist Jaleel Shaw as well as the bassist David Wong and its mainstay pianist, Martin Bejerano. Without a strong arrangement, it can get Coltrane-y in a hurry, which is not a philosophical or a historical problem: Mr. Haynes was a substitute in Coltrane’s quartet in the mid-’60s, and he learned from Coltrane just as Elvin Jones, that band’s regular drummer, had learned from him. On Saturday the young band sounded strong, particularly in its diabolical version of “My Heart Belongs to Daddy,” tied together by a roughed-up, highly changeable six-eight pattern, which Mr. Haynes ultimately took with him to center stage and rapped out with a palm on a microphone.

“Wow,” Mr. Haynes said, reacting to the total audience response. “And they said you didn’t have rhythm.”

The other group was ready from the start, charged and loose. In Sonny Rollins’s “Grand Street,” Mr. Marsalis and Mr. Garrett got into a strident back-and-forth, narrowing down until their improvisations mashed together. In Thelonious Monk’s “Monk’s Dream,” Mr. Marsalis fought back hard and gesturally against Mr. Haynes, but Mr. Pérez teased him, drawling and leaving gaps in the sound. (Here, and for the rest of the set, Mr. Marsalis leaned in close to the piano, keeping his head about a foot away from Mr. Pérez’s, invading his space and staring, following closely, laughing at the sly parts: something interesting was going on there.)

In “Stardust,” Mr. Marsalis brought off his best stuff: a solo of great dynamic range, of orderly melodic and rhythmic space. In “Bright Mississippi,” with the horns laying out, Mr. Haynes stayed focused on the clenched high-hat cymbal — à la his idol, the Basie-band drummer Jo Jones — and mixed up Cuban clave with swing rhythm in a performance that was all conviction: nothing clinical about it. And through Charlie Parker's "Segment" — Mr. Holland, with a big tone and a gathering insistence around drone notes, played like an earthmover, wincing and stomping his foot in the home stretch.