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"Only connect the prose and the passion," wrote British novelist E.M. Forster, "and both will be exalted." Zadie Smith's third novel, On Beauty, does, and they are. Beautifully written, it is — like her debut best seller White Teeth — essentially a story about families, expansive enough to encompass questions of race, Rembrandt, aging gracefully (or not), love, fidelity and, as the title suggests, recognizing what is truly beautiful and how we make it a part of our lives.

Smith, as she makes clear in her acknowledgments, is indebted to Forster for more than good advice. On Beauty is a rambunctious, 21st century take on Forster's own novel Howard's End. The debt is evident from the novel's first page. "One may as well begin with Jerome's e-mails to his father," it begins, updating Forster's blasé opener, "One may as well begin with Helen's letters to her sister." Thereafter, Smith revamps Forster's Edwardian battle of wills between the liberal-minded Schlegel sisters and the snobbish Wilcox clan into a modern academic feud that sweeps up the families of Howard Belsey, a white, English, radically-minded art-history professor at a prestigious New England liberal-arts college, and guest lecturer Monty Kipps, a black, traditionalist art historian who campaigns against affirmative action and other sacred cows of the liberal establishment. The story rambles on through renovations of several key Forster plot points: a broken engagement, a mix-up at a public concert, a Christmas shopping trip, and a stifled bequest. But by the time Smith's story is over it is clear that On Beauty is not just an homage but a work of real originality.

Smith has a virtuoso talent for capturing dialect, which makes her dialogue almost audible. Belsey's son Levi, a mixed-race child of privilege who takes a weekend job hustling knockoff handbags with Haitian immigrants on the streets of Boston, speaks perfect faux Brooklyn: "This ain't like workin' the counter at CVS! You hustling, man ... That's street." Belsey's southern teaching assistant Smith J. Miller spends half of his appearances trying to explain "pah-point" (Power Point) presentations to the Luddite professor.

More striking is Smith's ability to make her motley cast so much more than the caricatures they could become. Belsey's formidable African-American wife Kiki looms large. Her much-discussed 115-kg frame, once much smaller, practically becomes a character in and of itself. She is generally a warm, charming woman, but when angered, she reverts to her roots and, in her children's words, "comes over all Florida" (a Belseyism for going postal). In another work she might be reduced to a Big Momma from central casting, but while Kiki is humorous she is never laughable.

The book's lyrical skill, and the sweeping mix of ages, races and personal histories that populate the pages, is reminiscent of White Teeth. But On Beauty does not try to duplicate either the breakneck speed or the hilarity of Smith's first book. It's also strikingly different from her 2002 disappointment The Autograph Man, which degenerated into an artificially clever, pop-saturated riff on the anxieties of being twentysomething, and cast a shadow over her early successes. She still can't resist dotting the pages with inside references to everything from Tupac Shakur to Harold Bloom. But this time she shows greater restraint — and self-awareness.

In the past, Smith's chief flaw was similar to that of Zora Belsey, Howard's ambitious daughter, a sophomore at his university, who tries too hard to show off her literary cool. Through Zora, Smith now pokes fun at this fault. The girl's cringeworthy attempts to achieve bohemian-chic status are sensitively chronicled, and by the end of the tale — but not before one final, angst-ridden blowout — a wiser, smarter and much cooler young woman has emerged.

Smith has grown up, too. On Beauty, short-listed last week for the Man Booker Prize, is striking for the maturity of its sensibility and suggests that Smith is, indeed, a talent to watch over the long haul. You are not simply entertained by the writer's versatility and brilliant characters; you really care about these people. When they are stubborn you want to slap some sense into them. When they do good you cheer. And when they behave thoughtlessly you tend to forgive, because you can't escape the nagging suspicion that you yourself might not have behaved any better. The characters are, after all, only human, and when writing a novel one might as well begin with that.

• Zadie Smith's On Beauty is as well written as it is moving