It’s not exaggeration to say few rock ’n’ rollers command the stage the way Nick Cave does. It’s also probably safe to say no one has ever dominated the rest of the State Theatre like he did Saturday night.

Performing with a made-over lineup of his darkly elegant band the Bad Seeds, the Australian gloom-punk innovator was all over the place. He twice climbed deep into the audience for an entire song, his microphone cord stretching over fans’ heads and his lanky, Jagger-meets-Lurch figure looming ominously above the seats. He also repeatedly spilled over into the front-row orchestra pit, as if he wanted to personally tear out the seats there. “They did it in Milwaukee,” he quipped (knowing the State’s chairs were bolted down).

He’s a showman, sure, but rock stars with only half of Cave’s 56 years would be lucky to show his kind of physicality in concert. Which is to say nothing of the physicality of the music, as it veered from goosebump-inducing tender ballads to spine-rattling harsh rockers.

Cave opened with two of the sludgiest and most menacing songs from last year’s “Push the Sky Away” album, “We Know Who U R” and “Jubilee Street,” the latter of which built into a frantic climax that became the first of many breathless moments in the two-hour performance. His backlit shadow dominated the stage during the first two songs in darkly fantastical lighting, so when he took his first foray into the crowd during third song “Tupelo,” it was almost like Boris Karloff walking out of the screen during a screening of “Frankenstein.”

Saturday’s set list was laden with five songs off the overly drab “Push the Sky Away,” but they rose to life in concert. The Miley Cyrus-invoking “Higgs Boson Blues” was an especially dramatic highlight. “Let the damn day break,” Cave bellowed with his arms crossed into an X over his face.

With longtime guitarist Mick Harvey out of the Bad Seeds, many of the older tunes were reworked with less of a straight, rocky edge but no less roar, including “Mercy Seat,” which evolved from a prayer-like hush into hell-raising mayhem. Violinist/guitarist Warren Ellis (also known from the cult-loved Australian instrumental band Dirty Three) added rich textures throughout, lacing “From Her to Eternity” with a freaky staccato punch and shredding his bow in “Mercy Seat” in lieu of a guitar solo.

Cave had already proven his magic touch as one of rock’s greatest frontmen when he clasped hands with fans to climb deep into the seats a second time during the pre-encore finale “Push the Sky Away.” Nothing wrong with adding a little extra personal touch.