“I used to live alone before I knew you,” Leonard Cohen sings on “Hallelujah,” the closest he has come to a hit in 40-odd years of making music. The line is addressed to a lover, but it holds true for Cohen’s music; it may not have always been here, but it sure feels like it has. His songs, full of ambiguous imagery and palpable longing, are ideally designed to permeate memories, to insinuate themselves among private histories. The songs carry stories, his and yours, and to hear one is to find yourself suddenly submerged in a moment you thought had evaporated long ago.

A lot has been lived in the 15 years since Cohen’s last concert in America. Everyone currently under age 15 was born, most people born before 1920 died, and the era of Big Government ended and was resurrected. So when Cohen took the stage last Thursday at New York’s newly reopened Beacon Theater, all he had to do was remind the audience how much of their lives had played out with his songs in the background. This he did, with style: Over two sets, 26 songs, a few dry jokes (“I tried to study religion and philosophy, but cheerfulness kept breaking through”), and a spoken poem, Cohen showed an energy and focus that belied his 74 years. Dressed in a sharp suit and sharper hat, his always deep voice brought to new lows by age, Cohen performed classics from 1967’s “Songs of Leonard Cohen,” 2001’s “Ten New Songs,” and almost everything in between. But when he skipped offstage three and a half hours (and four encores) later, he had done more than entertain. With a quiet authority, Cohen argued for the necessity of lyricism in song.

Throughout the night, the old songwriter touched repeatedly on his favorite themes: sex, social dissolution and eschatology. On “I’m Your Man,” he mused mischievously about losing himself in desire: “If you want a boxer/I will step into the ring for you/And if you want a doctor/I’ll examine every inch of you/If you want a driver/Climb inside/Or if you want to take me for a ride/You know you can/I’m your man.” During “Democracy,” the bitter irony of which the cheering, Obama-struck audience chose to ignore, Cohen condemned the misguided self-congratulation of late-80s America: “From the wars against disorder/from the sirens night and day/from the fires of the homeless/from the ashes of the gay/Democracy is coming to the U.S.A.” He half-seriously broadened his apocalyptic portrait of societal cataclysm with “The Future”, eyes twinkling as he barked: “Give me crack and anal sex/ Take the only tree that’s left/ and stuff it up the hole/in your culture/Give me back the Berlin wall/give me Stalin and St. Paul/I’ve seen the future, brother/it is murder.” All was not gloom and doom, however, as Cohen, trapped as always in the space between romance and carnality, sang wistfully about Janis Joplin “giving me head on the unmade bed,” in “Chelsea Hotel No. 2.”

An acclaimed poet before he ever picked up a guitar, Cohen took care with his words, changing his phrasing both to accommodate his changed vocal range and to play with these familiar lines. Although his voice at times strained, like on the little-performed “Famous Blue Raincoat,” it never faltered, and occasionally hit notes in a register almost inhumanly low. With soaring backing vocals from Sharon Robinson and the Webb Sisters buttressing the creaks and rattles of his deep baritone, Cohen managed to sound like he had a much wider range than he does. His vocal limits did not detract from the quality of performance; if anything, it lent to his words a sense of incantation appropriate for an artist who relies as heavily as Cohen on religion for imagery and thematic material.

Backed by an ace band, whom he twice introduced individually and at length (his drummer as “the prince of precision, the keeper of time”), Cohen carried the crowd through his most famous songs and his greatest. “Hallelujah” provided the night’s emotional high point, but was nearly matched by a roaring “So Long, Marianne,” with people crowding the aisles and singing along, and a chilling rendition of “Anthem” that closed the first set. Cohen alternated between kneeling with emotion and holding his hat over his heart in what appeared to be a genuine show of appreciation and humility, the humility of an old man truly moved by the audience he commands.

And Cohen does command quite an impressive audience. At intermission, I ran into Josh Ritter, who at first could only repeat, “How about that show?” but recovered long enough to introduce me to his date and nod indulgently as I thanked him for his music. After the show, Rufus Wainwright begrudgingly gave me a cigarette (without offering a light), before being whisked away into the night by an extremely excited Tim Robbins. The people sitting next to me had flown in from Philadelphia; the people sitting next to them had come from England. There was not an empty seat to be seen, and reporters and photographers for lesser publications than this flooded the aisles and irritated many.

Pretty good for a 74-year-old poet.