Engel was the daughter of an admiral in the US Coast Guard and lived in various cities around the USA. After graduation from the University of Hawaii, she headed for New York, where she soon landed a role in the Off-Broadway revival of the musical revue "Lend an Ear" (1969). The following year, she could be seen as Minnie Fay in the Broadway production of "Hello, Dolly!" when Ethel Merman was in the title role. Engel then returned to Off-Broadway in the original production of John Guare's "The House of Blue Leaves" in 1971. This led to a guest shot on "The Mary Tyler Moore Show" playing a sweet-natured co-worker of Rhoda. The character clicked and before long, Georgette's original connection to Rhoda was long forgotten and she was Mary's friend and later romantic interest to Ted Baxter, eventually becoming his wife and mother of his children. When Moore retired her show, Engel followed co-star Betty White to her eponymous sitcom (CBS, 1977), but that show quickly fizzled.
She then appeared alongside Annie Potts as one of an ensemble of young women in Washington, DC, during World War II in "The Good Time Girls" (ABC, 1980), but that show was equally short-lived. She had the same luck with "Jennifer Slept Here" (NBC, 1983-84), in which Engel was the wife and mother of a family who buys a new house only to find it haunted by Ann Jillian. From 1991-1997, Engel had the recurring role of Shirley Burleigh, the jealous wife of the school administrator on the ABC sitcom "Coach." Engel would appear sporadically in films--including voicing a giraffe in the Eddie Murphy comedy "Dr. Dolittle 2" (2001) and as a sweet natured boutique owner in the Cameron Diaz vehicle "The Sweetest Thing" (2001)--before landing her next memorable sitcom role, appearing frequently as Robert Barone's mousy mother-in-law Pat McDougal in the hit series "Everybody Loves Raymond" from 2003 throught the series finale in 2005.
Engel has only occasionally appeared in TV-movies and feature films. She was Claire Ruth, wife of The Babe, in "Love Affair: The Eleanor and Lou Gehrig Story" (NBC, 1978). Her work on the big screen began in 1971 with a role as a sympathetic friend to the heroine in Milos Forman's first American film, "Taking Off". Engel provided the voice of Love a Lot in "The Care Bears Movie" (1985), and had supporting roles in "Papa Was a Preacher" (1987) and "Signs of Life" (1989). She also traveled to France to play a small role as "a woman" in "Un Homme est mort" (1973).
An accomplished singer and dancer, Engel has only rarely been able to showcase these talents on TV, but did a rendition of "Steam Heat" in an episode of "The Mary Tyler Moore Show" She frequently appeared in variety specials headlined by Dean Martin and returned to Broadway succeeding Denny Dillon as a singing and dancing mechanic in "My One and Only".