Lavin died in Los Angeles on Sunday of complications from recently discovered lung cancer, according to her representative, Bill Veloric.
A success on Broadway, Lavin tried her luck in Hollywood in the mid-1970s.
She was chosen to star in a CBS sitcom based on Alice Doesn't Live Here Anymore the Martin Scorsese-directed film that won Ellen Burstyn an Oscar for playing the waitress in the title.
The title was shortened to Alice and Lavin become a role model for working mothers as Alice Hyatt, a widowed woman working in a roadside diner while raising a 12-year-old son.
The show, with Lavin singing the theme song There's A New Girl In Town, ran from 1976 to 1985.
Variety magazine listed it among the all-time best workplace comedies.
Lavin soon went on to win a Tony for best actress in a play for Neil Simon's Broadway Bound in 1987.
She was working as recently as December promoting a new Netflix series in which she appears, No Good Deed, and filming a forthcoming Hulu series, Mid-Century Modern, according to Deadline, which first reported her death.
Lavin grew up in Portland, Maine, and moved to New York City after graduating from the College of William and Mary. She sang in nightclubs and in ensembles of shows.
Famous producer and director Hal Prince gave Lavin her first big break while directing the Broadway musical It's a Bird ... It's a Plane ... It's Superman.
She earned a Tony nomination in Simon's Last of the Red Hot Lovers in 1969 before winning 18 years later for Broadway Bound.
In the mid-1970s, Lavin moved to Los Angeles. She had a recurring role on Barney Miller and in 1976 before being chosen to star in Alice.
She returned to TV in 2013 in Sean Saves The World, starring Will & Grace's Sean Hayes, a show which lasted a season.
Back on Broadway, Lavin later starred in Paul Rudnick's comedy The New Century, had a concert show called Songs & Confessions of a One-Time Waitress and earned a Tony nomination in Donald Margulies' Collected Stories.
She also appeared in the film Wanderlust with Jennifer Aniston and Paul Rudd, and released her first CD, Possibilities.
She played Jennifer Lopez's grandmother in The Back-Up Plan.
When asked for guidance from young female actors, Lavin stressed one thing.
"I say that what happened for me was that work brings work. As long as it wasn't morally reprehensible to me, I did it," she said in 2011.
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