Don DeLillo’s novels are celebrated for their openings, the best of which are set in his native New York City. Mao II memorably begins with the wedding of thousands of Moonies at Yankee Stadium, Libra with the haunting image of a young Lee Harvey Oswald riding a Bronx subway. DeLillo’s master-work, Underworld, commences with the most astonishing set piece in modern American fiction – a 60-page account of a famous baseball game played in New York’s Polo Grounds.

It is hardly surprising, therefore, that the author’s searing, profoundly unsettling Falling Man opens in Manhattan at the worst moment in the city’s history. “It was not a street any more but a world, a time and space of falling ash and near night,” DeLillo writes. “The roar was still in the air, the buckling rumble of the fall.” It is, of course, mid-morning on September 11, 2001. Amid the smoke and ash, a lawyer named Keith Neudecker limps uptown after narrowly escaping from his office in the upper reaches of one of the now-vanished towers. He eventually arrives at the apartment of his wife Lianne and their son Justin. Legally separated at the time of the attack, the couple is immediately drawn back together.

From the first, DeLillo makes clear that this pair, like their nation, will long bear the scars of what has just happened. As Keith is treated for his flesh wounds, a doctor explains how victims of suicide bombings will sometimes “develop bumps, for lack of a better term, and it turns out this is caused by small fragments, tiny fragments of the suicide bomber’s body . . . they get wedged, they get trapped in the body of anybody who’s in striking range . . . they call this organic shrapnel”. Although Keith is quickly assured that he will bear no such physical scars, a psychic version of organic shrapnel gradually afflicts him and those close to him. Keith yearns to be with his family, but still enters into an affair with the woman whose briefcase he mistakenly carried from the tower. Obsessed with the mechanics of chance, he quits his job and travels to Las Vegas to play poker. Lianne also bears spiritual wounds. She irrationally begins to dread the early onset of the neurological disease that killed her father, and even assaults a neighbour who callously plays Middle Eastern music.

Their seven-year-old son Justin, meanwhile, starts to speak ominously about his fear of a stranger named Bill Lawton, whose name turns out to be a bastardisation of a rather more sinister character. Nina, Lianne’s cosmopolitan mother, gives in to the siren call of angry intolerance, thereby destroying her long-standing love affair with Martin, a Swiss art collector whose alliance with 1970s European terror groups causes him to empathise with the attackers. It is left to him to give voice to one of the deepest splinters of doubt that have lodged beneath the skin of DeLillo’s tormented characters. “But that’s why you built the towers, isn’t it?” he asks Nina during an angry confrontation. “Weren’t the towers built as fantasies of wealth and power that would one day become fantasies of destruction? You build a thing like that so you can see it come down. The provocation is obvious. What other reason would there be to go so high and then to double it, do it twice? It’s a fantasy, so why not do it twice? You are saying, Here is it, bring it down.”

Such glimpses of the big picture are rare, however. Instead, DeLillo chooses to work in miniature – to devastating effect. Even the novel’s quietest moments are ripe with ominous meaning. In one apparently negligible scene, Keith and his friends gather for a weekly poker game a few weeks before the attack. As they smoke cigars and drink whisky, they tease a colleague of Keith’s named Rumsey about his name. “Someone told Rumsey one night, it was Dockery the waggish adman, that everything in his life would be different, Rumsey’s, if one letter in his name was different. An a for the u. Making him, effectively, Ramsey. It was the u, the rum, that had shaped his life and mind,” making him, in other words, clumsy and passive. After one of the hijacked planes strikes the World Trade Center, falling debris kills Rumsey in his small office at the end of the corridor, leaving Keith, who occupies a choicer room, to wonder if his friend died for a vowel; if a more assertive “Ramsey” would have insisted on another office, and survived.

Bleak mystery also surrounds a performance artist named David Janiak, who begins to appear around New York soon after 9/11. Dressed in a suit and calling himself Falling Man, he uses a harness to hover above the city in gruesome homage to those who jumped from the towers. He never explains himself, never publishes a manifesto. Spectators are left to guess at his motives, which are perhaps nothing more than a primal emanation of the city’s afflicted psyche.

But Janiak is not the novel’s most problematic character. This dubious honour goes to Hammad, one of the musclemen on Mohammed Atta’s doomed plane. In brief, oblique scenes, he is depicted plotting in Hamburg, training in Florida, and finally guarding the cockpit door as the jet glides down the Hudson corridor. “Every sin of your life is forgiven in the seconds to come,” Hammad thinks as Atta shouts his final prayers from the plane’s controls. “There is nothing between you and eternal life in the seconds to come.” And then the plane strikes. DeLillo does not wonder whether or not the would-be martyr ascends to paradise. What he does establish beyond doubt is that Hammad and his brothers have managed to live on after their deaths – as a form of organic shrapnel. They, more than David Janiak or Keith’s doomed colleagues, are this unforgettable novel’s true falling men.

FALLING MAN by Don DeLillo

Picador £16.99 pp246

Buy the book here at the offer price of £15.29 (inc p&p)

Times Recommends

• The 100 Best Books of the Decade
• The Times picks the 50 best paperbacks of 2009
• The conversation: James Ellroy