Harper was born on August 15, 1950, in Mammoth Spring, Arkansas, the daughter of Rosemary (née Langston) and Ed Washam. Most members of her family were quilt makers. On her own time she liked to sit on the porch swing and read. She graduated from high school in 1968. She attended Arkansas State University-Beebe, where she performed in several plays, as well as Southwest Missouri State University (now Missouri State University) in Springfield, Missouri, where she graduated with a degree in education.
Harper began acting in theater productions, theme parks (including Dogpatch, USA and Silver Dollar City), dinner theatre, and children's theatre. She had given up hopes of an acting career and was working for a financial institution in Texas. The institution wanted to produce a TV spot and asked her to be in the spot, which she accepted. In a twist of fate, a casting person with Tender Mercies had to spend the night in Dallas and saw Harper's spot on TV. She called Robert Duvall and arranged an audition. Director Bruce Beresford was impressed with Harper and cast her in the lead female role of Rosa Lee, the young widow and mother who marries country singer Mac Sledge. Beresford said that Harper brought a kind of rural quality to the role without coming across as simple or foolish. He said of Harper, "She walked into the room and even before she spoke, I thought, 'That's the girl to play the lead.'" Harper did not realize this, and recalled shortly after the film's release, "After I did the final screen test, I went to see Breaker Morant and started sobbing uncontrollably halfway through it. A friend had to take me home, and I kept crying, 'You don't understand! They're not gonna let me do this part!'"
Tender Mercies was Harper's feature film debut. She later said that she was so excited about the role that she bit her script just to make sure it was real, and she was so nervous that during her first take she feared the filmmakers would "come to their senses and say, 'We're sorry, we made a terrible mistake.'" Duvall, who played the lead role of Mac Sledge, did his best to help Harper in her first film role. During one scene in which Mac Sledge and Rosa Lee were fighting, Duvall yelled at a make-up artist in front of Harper specifically to make her angry for the scene; Duvall apologized to the make-up artist after the scene was shot. After filming, Duvall said Harper did a very good job, and he felt her rural past in Arkansas helped her in the part. She earned a Golden Globe Award nomination for the role. Duvall won the Academy Award for Best Actor for his performance.
Harper appeared in the TV mini-series Chiefs (1983) and Celebrity (1984), as well as many television movies including Starflight: The Plane That Couldn't Land (1983) and Reckless Disregard (1985). In 1983, she appeared in the full-length feature Silkwood. In 1986, Harper was nominated for the Academy Award for Best Supporting Actress for her work as Chick Boyle in Crimes of the Heart, which was directed by her Tender Mercies director Bruce Beresford. She later played parts in Ishtar (1987), Far North (1988), The Man in the Moon (1991), The Jackal (1997) and Loggerheads (2005). She also took part in Michael Jackson's Black Or White (1991) musical minifilm. Harper had a regular role on the CBS series Christy, from 1994-95. Her roles have frequently been that of a Southern lady, although she had worked to lose her Arkansas accent. She also had a recurring role on another CBS television series, Early Edition, from 1996 to 2000. She portrayed the mother of lead character Gary Hobsen. Harper shared a Screen Actors Guild Award (in the Best Ensemble Cast category) with her fellow cast members in the Oscar-winning film No Country for Old Men, in which she played the wife of Tommy Lee Jones. She had the recurring role of Mrs. Pinkman on Breaking Bad, appearing in the first three seasons.