The Tennessee native used her unmistakable Southern accent and style on series like "Diff'rent Strokes" and "Filthy Rich" before landing the role of Julia Sugarbaker on "Designing Women," the CBS sitcom that ran from 1986-1993 and had an endless life in reruns.
She was nominated for an Emmy in 2007 for a celebrated seven-episode guest stint on the ABC hit "Desperate Housewives."
"This has been a terrible blow to our family," Carter's husband and fellow actor Hal Holbrook said in a written statement. "We would appreciate everyone understanding that this is a private family tragedy."
Carter lived with Holbrook in the Los Angeles area but traveled home to Tennessee several times a year. It was not clear why she was in Houston when she died.
She married Holbrook in 1984. The two had met four years earlier while making the TV movie "The Killing of Randy Webster," and although attracted to one another, each had suffered two failed marriages and were wary at first.
They finally wed two years before Carter landed her role on "Designing Women." Holbrook appeared on the show regularly in the late 1980s as her boyfriend, Reese Watson.
The two appeared together in her final project, the 2009 independent film "That Evening Sun," shot in Tennessee and based on a short story by Southern novelist William Gay.
The second of three children, Carter was born in 1939 in McLemoresville, Tenn.
Carter was the daughter of a grocery and department store owner who died just three years ago at 96. She said at the time of his death that he taught her to believe in people's essential goodness.
"When I asked him how he handled shoplifting in his new store, which had a lot of goods on display, making it impossible to keep an eye on everything, he said, 'Most people are honest, and if they weren't, you couldn't stay in business because a thief will find a way to steal,"' Carter said. "'You can't really protect yourself, but papa and I built our business believing most people are honest and want to do right by you."'
Carter grew up in Carroll County and made her stage debut in a 1960 production of "Carousel" in Memphis. It was the beginning of a decades-long stage career in which she relied on her singing voice as much as her acting.
She appeared in TV soap operas in the 1970s, but did not become a national star until her recurring roles on "Diff'rent Strokes" and "Filthy Rich," in the 1980s.
Those two parts led to her role on "Designing Women." Carter and Delta Burke played the sparring sisters who ran the firm. The series also starred Annie Potts and Jean Smart.
The show was unmistakably a comedy but tackled such topics as sexism, ageism, body image and AIDS.
"It was something so unique, because there had never been anything quite like it," Potts told The Associated Press at a 2006 cast reunion. "We had Lucy and Ethel, but we never had that exponentially expanded, smart, attractive women who read newspapers and had passions about things and loved each other and stood by each other."
Carter appeared on the drama "Family Law" from 1999 to 2002, and in her last major TV appearance she played Gloria Hodge, the surly mother-in-law to Marcia Cross's Bree on "Desperate Housewives."
Carter said the role was far from the kindly woman she played on "Designing Women."
"It's a vast difference," Carter said while filming the series. "Gloria Hodge doesn't have any redeeming qualities except her intelligence."
Besides Holbrook, Carter is survived by daughters Mary Dixie and Ginna.