Leave it to Radiohead to make a musical left turn just when it seemed that the world had caught up to its frigid, electronics-fueled, apocalyptic visions.

At its Tuesday night show at Madison Square Garden, its first American show in four years and the kickoff to the North American leg of its “A Moon Shaped Pool” tour, their sound was once again heroic, warmer and fuller and more about guitarist Jonny Greenwood than it has been in more than a decade. Maybe even more surprising was how much fun the band, known for its serious statements, had onstage.

Singer Thom Yorke pointed playfully at members of the audience, occasionally made machine noises in place of talking to the audience and even faked a pratfall. By the time he was proclaiming, “Ice age coming! Ice age coming!” in “Idioteque,” he was bouncing around on the stage and shaking his maracas. (Not a metaphor, actual maracas.)

Though the band took a risk by opening the show with the first five songs from the new “A Moon Shaped Pool” album, it worked. The new material was strong and arranged to sound even more powerful than it did on the record and starting with a massive version of “Burn the Witch” the momentum continued to grow.

The middle of the main set hit a crescendo with a singalong version of “No Surprises” that was awash in acoustic guitars rather than the original’s icy electronic sounds from “OK Computer.” During “Myxomatosis,” Yorke was dancing around like a maniac and leading the crowd’s arm-waving.

Those moves, along with the band’s grateful reactions to the huge ovations from the crowd, may sound conventional, though, of course, Radiohead is anything but. They left their most popular songs off the set list and even skipped the best song from “A Moon Shaped Pool” (the infectious, danceable “Identikit”), but it hardly mattered.

This new incarnation of Radiohead is built for large crowds and even larger spaces, making the most of the audience’s energy and singalong support. After years of worrying about what success would do to them, Radiohead seems to have embraced it now and that has only made them stronger.

(Radiohead plays Madison Square Garden again Wednesday night.)

SETLIST: Burn the Witch / Daydreaming / Decks Dark / Desert Island Disk / Ful Stop / Lotus Flower / The National Anthem / 15 Step / No Surprises / Tinker Tailor Soldier Sailor Rich Man Beggar Man Thief / Separator / Planet Telex / The Numbers / 2+2=5 / Everything in Its Right Place / Myxomatosis / Idioteque // ENCORES: Let Down / Present Tense / Paranoid Android / Nude / Bodysnatchers / Bloom / Street Spirit (Fade Out)