She is best known for having played Georgette Franklin Baxter in the sitcom The Mary Tyler Moore Show from 1972 to 1977, Pat MacDougall on Everybody Loves Raymond from 2003 to 2005, and Mamie Sue on Hot in Cleveland from 2012 to 2015.

She moved to New York City in 1969, appearing off-Broadway in Lend an Ear, and for a year as Minnie Fay in the Broadway production of Hello, Dolly!, starting in December 1969.

[5] A 1971 off-Broadway production of The House of Blue Leaves eventually played in Los Angeles, where Engel was seen by Mary Tyler Moore and her husband, producer Grant Tinker, her soon-to-be employers.

[13] Engel received consecutive Emmy Award nominations as outstanding guest actress in a comedy series in 2003, 2004, and 2005 for her role on Everybody Loves Raymond as Robert Barone's mother-in-law, Pat MacDougall.

[14] Engel made her "big screen" debut in Miloš Forman's first English-language movie Taking Off (1971),[15] playing "Margot", a performance that earned her a BAFTA nomination for best supporting actress.

Her other film appearances include The Outside Man (1973),[16] Papa Was a Preacher (1987),[17] Signs of Life (1989),[18] The Sweetest Thing (2002),[19] and the made-for-TV movies The Day the Women Got Even (1980)[20] and A Love Affair: The Eleanor and Lou Gehrig Story (1978).

[38] Engel appeared in the new Annie Baker play John, which opened off-Broadway at the Signature Theatre on July 22, 2015 (previews), directed by Sam Gold.

[41] Engel starred in the musical Gotta Dance, which premiered at the Bank of America Theatre, Chicago on December 13, 2015, and ran until January 17, 2016.

The musical was directed and choreographed by Jerry Mitchell, with a book by Chad Beguelin and Bob Martin, and the score by Matthew Sklar and Nell Benjamin.