Equipped with a sweet disposition and heavenly voice, Ms. Cook was possibly the most all-American, apple-pie female lead the Broadway musical stage ever saw. She played most of her important roles while in her 20s and 30s. These included two landmark musicals, She Loves Me and The Music Man—she was the original Marian the Librarian—as well as the flawed masterpiece Candide, and the lesser-known shows Plain and Fancy, Flahooley, and The Gay Life. She introduced such standards as “Till There Was You,” “My White Knight,” “Ice Cream,” and “Glitter and Be Gay.”

Harold Prince, who directed She Loves Me, once said, “I’ve heard a hundred versions of ‘Ice Cream’ but none touches Barbara Cook’s. It must be that the music and lyrics are absorbed by her characters to such an extent they preempt their authorship.”

By the early ‘70s, however, the stage roles had dried up—so she forged a second act to her career as a premier interpreter of the songs of the theatrical stage she had left behind. In 1975, she made her debut as a song stylist at Carnegie Hall, and critics took new notice of her. She returned to the hall again in 1980. By the 1990s and 2000s, she was regularly headlining the country’s best cabaret spots and concert halls.

Ironically, she said this phase of her stage life was when she began performing the meaning of a lyric. “When I first started out,” she recalled. “I didn’t give much thought to acting a song. That evolved. Now I think of it as living inside a song and singing my way out—inhabiting it, feeling it, making it felt from my core to your core. That’s the only way I can explain it.”

Barbara Cook was born on October 25, 1927, in Atlanta, Georgia, the daughter of a traveling hat salesman and an operator for Southern Bell. When Ms. Cook was three, she contracted whooping cough. Her younger sister, Patricia, only 18 months old, had pneumonia, but then Patricia caught the whooping cough, too, and died.

Young Barbara fell in love with the opera when she was eight or nine listening to the family radio. “We were so poor we didn’t have a record player of any kind whatsoever,” she recalled. “The radio was my lifeline, that and films. I just don’t know where that came from. I didn’t even know anybody who liked opera or classical music. I don’t even remember a friend who particularly liked classical music.”

In 1948, she moved to New York City. She supported herself as a typist the first few years, auditioning whenever she could. Her Broadway debut was in the 1951 show Flahooley, which ran but a month. Sammy Fain and E.Y. “Yip” Harburg threw her a couple of songs—“He’s Only Wonderful” and “Here’s to Your Illusions”—with which she shrewdly upstaged the four-octave warblings of Flahooley’s nominal star, Yma Sumac.

As the resident ingénue in Plain and Fancy, she won a Theatre World Award as a Promising Personality of the 1954-1955 season. Wherever she landed after that, she seemed to find the archetypal ingénue role waiting for her—a circumstance that often frustrated her and which she sent up later as a cabaret artist in the satiric David Zippel number “The Ingenue.” (The song includes a comic zinger about Shirley Jones doing the film version of The Music Man.)

Ms. Cook’s most famous role, and the part for which she is best remembered, is Marian Paroo, the skeptical, seemingly straight-laced librarian of River City, Iowa, who is romanced by the fast-talking music salesman Harold Hill, played by Robert Preston. She won a Tony Award for her performance. “He was an incredibly consistent performer and a joy to work with,” she said of Preston. “He brought such energy to the show. I think that’s why it ran as long as it did.”

Candide, in 1956, was arguably her most challenging assignment, a musically intricate reworking of Voltaire’s satire of a young man’s picaresque adventures. Ms. Cook played Candide’s fickle, feckless love object, Cunegonde. Leonard Bernstein is said to have shaped the operatic comic song “Glitter and Be Gay” around Ms. Cook’s voice and phrasing. She also acted in City Center revivals of Carousel and The King and I.

The 1961 musical, The Gay Life, based on Arthur Schnitzler’s Anatol, is mostly forgotten today, but the CD reissue of its original cast album is a favorite of fans, and shows off Ms. Cook’s delicacy and fire in a variety of late-career songs by lyricist Howard Dietz and composer Arthur Schwartz. Among her choice numbers in the show: “Magic Moment,” “Something You Never Had Before,” “I Wouldn’t Marry You,” “The Label on the Bottle” and “You’re Not the Type.”

In 1963’s She Loves Me, she played opposite Daniel Massey as one of two young colleagues in a Budapest perfume shop who detest each other, not knowing they are secretly romantic pen pals. In the show, she realizes her sudden love for the man she once hated in “Ice Cream,” a song ostensibly about a gift of sweets brought by Massey. (It being a Stephen Sondheim favorite, she reprised it later in her cabaret act called Mostly Sondheim, in which she performed songs both by the composer and tunes Sondheim wished he had written.)

Barbara Cook married the acting teacher, David Legrant, in 1952 and they had a son, Adam. The two divorced in 1965. Around that time, her career began to slow down, and she started to put on weight, further hampering her employment potential. “If you’re happy, you eat. If you’re sad, you eat,” she recalled. “You lose a job, you eat. You get a job, you eat. It’s, you know, it’s addiction.” She also admitted to drinking in excess, calling herself a “nonfunctioning alcoholic.” When her son Adam was 14, he went to live with his father.

“I was really in bad shape,” she told the New York Times. “I would get up to get him off to school and go back to bed and sleep till he was about to come home. I’d set the clock and try to be dressed, kind of together when he came home from school. The house was a wreck, terrible.”

“It’s hard to deal with it,” she told Playbill in a 2016 interview about the publication of her memoir. “And yet, I wanted to be honest. And I’m hoping maybe people who are reading the book who need help will have an open mind and hopefully be helped. That’s the final thing I thought about writing the book—because I put it off a long time, and I didn’t really want to do it because I knew how hard it would be. And then finally it occurred to me that if somebody’s in trouble and they have an open mind, maybe there are things in the book that could help them. Maybe they could see that you can have a second life. And you can stop drinking. It ain’t easy, boy.”

Ms. Cook struggled to find a new direction, not wanting to return to the sort of ingénue parts she had been doing. Finally, her career was reborn on January 26, 1975, during a legendary concert at Carnegie Hall. Critics hailed her performance. A recording of that concert was released, selling well. She stopped drinking in 1977.

Helping her put the Carnegie engagement together was accompanist Wally Harper, who had suggested the idea. Ms. Cook and Harper played at a club called Brothers and Sisters, on Restaurant Row in Midtown in the early ‘70s. There, Herbert Breslin, Luciano Pavarotti’s manager, heard them and booked them into Carnegie Hall. Thereafter, they forged a collaboration that lasted three decades, until his death in 2004. “There’s no way to quantify” what Mr. Harper contributed, Ms. Cook said in 2002. “We do it together.”

Observers said that her artistry seemed to be renewed recently when she teamed with music director Lee Musiker.