Elizabeth Hardwick’s tempestuous marriage to Robert Lowell drew attention away from her own powerful work.

No one knows exactly what is meant by “a writer’s writer,” but it seems to fit the literary accomplishments of Elizabeth Hardwick. She once wrote that “the true prose writer knows there is nothing given . . . until an assault has taken place, the forced domination that we call ‘putting it in your own words.’ ” Hardwick published stories, novels and a short, original account of Herman Melville. But she is mainly and rightly thought of as an essayist who over the course of half a century wrote about a rich variety of subjects—fiction, politics, social events, and places, perhaps most notably the state of Maine, where she spent many summers. She is not easy to categorize except that her essays, many of which appeared in the New York Review of Books, where she was a founding editor, were always the occasion for crisp observations and ironic formulations that invite a reader to find pleasure in the facility of her sentences, the distinctness of her tone. She once wrote that her friend Mary McCarthy wanted her criticism to be “noticed,” to be “spectacular.” Hardwick is more relaxed in her confident address.

Hardwick’s famous marriage to the poet Robert Lowell, in all its ups and downs, has threatened to overshadow her own literary achievement to such an extent that Cathy Curtis takes care to warn us that “A Splendid Intelligence: The Life of Elizabeth Hardwick” includes “only as much information about her famous husband . . . as is necessary to tell the story of her life.” The author of three studies of somewhat critically neglected women artists, Ms. Curtis is aware that her subject is in danger of subordination to Lowell, an especially glamorous figure who has been treated in more than one biography.

Hardwick’s early years (she is always “Elizabeth” to her biographer) are unexceptional: the eighth child in a family that would see three more. During her college years at the University of Kentucky she was a serious student, disdaining extracurricular activities, not joining a sorority. “A Southern woman who didn’t fit the Southern sensibility” is Ms. Curtis’s summation. The intellectual event that stands out from these years was a course she took in contemporary poetry with the already well-known poet-critic John Crowe Ransom, in Hardwick’s words a “small and very precise man . . . very refined, very complex man” who taught her how to read a poem. That experience represented her effort, says Ms. Curtis, “to become the cultured, sophisticated person she wanted to be.”

She soon discovered, as a graduate student at Columbia, that this sophisticated person didn’t need—indeed would be better off without—professorial credentials; so she dropped out of candidacy for the Ph.D. and set up as a writer of fiction and criticism, while she visited the city’s jazz clubs where the great Billie Holiday prevailed. In her novel of some years later, “Sleepless Nights,” she brings the singer to life: “The spotlight shone down on the black, hushed circle in a café; the moon slowly slid through the clouds. Night—working, smiling, in makeup, in long silky dresses, singing over and over, again and again.” Ms. Curtis focuses only lightly on Hardwick’s love affairs in these New York years (the name of Allen Tate is mentioned). Her literary success was signaled by her 1945 novel, “The Ghostly Lover,” praised by Philip Rahv and his associates at Partisan Review.

Her most significant connection was with Lowell, who wrote about how he was overcome by Hardwick’s presence as he “outdrank the Rahvs in the heat / of Greenwich Village, fainting at your feet.” They were married in 1949, by which time Lowell was exhibiting the pattern of exultation followed by breakdown and depression that would characterize his life. A chapter in the biography, “European Immersion,” surveys the two and a half years the couple spent in Europe, part of it in Amsterdam, where for some reason Lowell had decided they must live. Hardwick felt the burden: “Now back at the grind like a Buffalo housewife, except that I don’t speak the language,” she wrote McCarthy. The daily hour and a half spent food shopping in her “halting Dutch” gave her “the kind of anxiety usually felt only for the last judgment” but produced only “strange cuts of meat in ‘uncookable shapes.’ ” Her wry exasperation was stimulated by living with someone who avoided “the grind” and likewise didn’t speak the language. Ms. Curtis speaks more strongly than is her wont when she quotes from a Lowell letter that sounds “needy,” “arrogant” and “manipulative”: “Why couldn’t he see that traveling with another person meant not always doing everything your driven personality demanded?” Nothing in Hardwick’s relationship with Lowell suggests that there was ever an answer to such questions.

At the heart of this biography is the period from 1949 to 1972, which saw Hardwick establish herself as a critic and novelist, and coincides with her marriage to Lowell. Hardwick’s career burgeoned as her work began to appear in the Partisan Review, the New York Times Book Review and, beginning in 1963, the New York Review of Books. In the same period there is the birth of her daughter, Harriet, preceded and followed by painful separations and reunitings with her husband. (Saskia Hamilton’s recent edition of their correspondence, “The Dolphin Letters,” is a full account of their final split.) Ms. Curtis’s narrative comes alive when she quotes Hardwick’s devastating, strongly turned formulations about her husband. In what the biographer calls “a stab at black humor,” Hardwick sees “that she couldn’t divorce someone who was not the person she married but rather ‘some awfully fatuous man I alas happen to be temporarily connected with.’ ”

Ms. Curtis is seldom moved to disagree with or correct Hardwick’s accounts, nor to persevere in a close look at how Hardwick’s sentences work to form convincing portraits of her subjects. She quotes a complicated sentence from Hardwick, like one about Bernard Berenson, who “lived with the silky regularity and pleasurable concentration of energies that are at once opulent and sacrificial—the prudence of the sensual,” but then proceeds without further comment to the next event.

When “Sleepless Nights” was published in 1979, the response was enthusiastic, a fact Ms. Curtis demonstrates with a list of friendly names who said nice things about it. That list includes Susan Sontag, Joan Didion, Edmund White, the Village Voice, New York magazine, Newsweek and various other reviewers and reviews from American and English publications. She follows with a summary of what “others” took the book to be and what “some insisted” about it. This may be a case in which more means less, when the parade of accolades is substituted for close engagement with the writing.

It is a problem any biographer, certainly one as scrupulous as Ms. Curtis, has to face. I think she would agree in calling Hardwick, with her “discrete observations and unusual metaphors,” a writer’s writer, but critical demonstration is needed to make the label stick, something that can’t be done by a biography concerned to get all the names in.

Mr. Pritchard is Professor of English Emeritus at Amherst College.