NEW YORK—As the Strokes raced through post-punk hit after hit at their concert at the Hammerstein Ballroom in New York last Saturday night, singer Julian Casablancas, normally the picture of detached cool, showed some emotion.

He mumbled “All these nights have been good, but you guys have been the best,” and the crowd roared back. Six years after being proclaimed the next saviors of rock, the group proved as worthy of that title as ever.

Touring in support of their third album, “First Impressions of Earth,” Manhattan’s favorite sons looked confident and sounded enormous. Dressed mostly in black, the Strokes concluded a three-night stand at the 3,000 person venue.

The Strokes have clearly grown up since the release of their stripped-raw 2001 debut “Is This It.” Then, the skinny-tie-wearing partiers, barely beyond their teens, rejected million-dollar studio techniques for a bare, garage-rock sound.

But the five subsequent years have witnessed a significant evolution for the band. They’ve developed a fuller sound, both on record and on stage, and perform more challenging instrumental parts and more expressive, emotional lyrics. What the Strokes have since lost in edge and youth they have gained in confidence.

Despite their change in sound, the Strokes pulled their tried-and-tested tricks out of the hat on Saturday. The precise, driving bass lines of Nikolai Fraiture on bass and Fabrizio Moretti behind a raised drumset got the floor pounding.

The two guitarists’ now-infamous interlocking parts sounded better live than on record: Albert Hammond Jr. laid down the rhythmic chords while effortlessly cool, waif-thin Nick Valensi fashioned melodic arpeggios on top.

Throughout the concert, the band led the emotions of the audience up and down. Casablancas, known for his bizarre drunken stage mumbles and tendency to avoid eye contact with his audience, was reticent at times. As red lights shot up and down the stage, he gave an introverted but moving vocal performance in “12:51.”

But soon enough, buoyed by the crowd, Casablancas abandoned his reserve and sang his heart and lungs out. In “Room on Fire,” he collapsed to his knees, screaming, “The night’s not over yet,” as the jubilant crowd lapped up the singer’s newfound on-stage exuberance.

Bringing the energy down, Valensi crouched behind a white synthesizer and Casablancas took the center spotlight in the soft “Ask Me Anything,” while the rest of the band exited the stage. The blue glow that cast across the audience from dozens of cell phones was a fitting post-millennial substitute for the yellow-orange flicker of lighters of the bygone 1990s.

Yet soon enough, emotions pushed to fever pitch with the performance of “Ize of the World,” one of the strongest tracks from the new album. The guitarists unleashed, twisting and jumping as Casablancas nailed the impossibly high vocal line.

The audience, comprised of both long-time and new fans, was uniformly ecstatic throughout the show.

Brandon Jernigan, 20, who had never seen the Strokes in concert before, summed up the experience of most of the concertgoers when he told The Crimson, “The show kicked ass.”

Maggy Schultz, 17, who told The Crimson that she has seen the Strokes before “four or five times,” said, “What struck me about it was that their audiences used to be filled with rich white kids. Now they’ve diversified.” Scanning the audience, she remarked, “I see people of all ages and races. It used to be just private-school rock.”

After the concert, the Strokes’ manager, Ryan Gentles, spoke to The Crimson. Originally in charge of booking at the Mercury Lounge in the East Village in 2000, Gentles was so impressed by the Strokes that he quit his job to manage them.

“Tonight’s crowd was the best crowd yet of the three sold-out nights,” he said. “I didn’t know if the city would welcome us back with open arms. But we had a clean sweep.”

“It’s a tough city. New Yorkers have entertainment here eight days a week,” Gentles said. “You’d got to do something special to get people’s attention.”

Though New York is the place to make it, it’s also the place to be broken. In a judgmental, fast-paced city known for spitting out new trends and soon abandoning them, the Strokes have managed to maintain their aura of cool in this city for six years. If they continue to put on shows like Saturday’s, then they’ll be around for a long time more.