After graduating from the ballet school in 1967, she earned a theater degree at the University of Hawaii. She then landed a part in a Milos Forman movie, “Taking Off,” whose screenwriters included John Guare. Once “Dolly” ended its run in 1970, that connection proved auspicious.

“I was walking down the street one day after ‘Dolly’ closed to cash my unemployment check for $75,” Ms. Engel told The Toronto Star years later, “when I ran into John and he told me I had to be in his play ‘The House of Blue Leaves.’ I was so thrilled, until I got my first paycheck. I was making $74, one dollar less than unemployment.”

The payoff came when Ms. Moore and her husband, the producer Grant Tinker, saw Ms. Engel in that play in Los Angeles. The role of Georgette soon followed.

Ms. Engel also had recurring roles on “Jennifer Slept Here” in the 1980s and “Coach” in the 1990s, among other shows.

In the 1990s she toured with versions of the “Nunsense” musical theater franchise, and in 2003 she joined an all-star 20th-anniversary “Nunsense” touring production that also featured Kaye Ballard, Mimi Hines, Darlene Love and Lee Meriwether.

Ms. Engel was in the original Broadway cast of “The Drowsy Chaperone” in 2006, playing a dotty woman named Mrs. Tottendale. The role required her to aim repeated spit takes at her character’s butler. She ended up doing a lot of spitting: After originating the role on Broadway, she joined the tour and stayed with it for more than a year.

“At first, I was getting more on me than on the other person,” she told The Atlanta Journal-Constitution in 2008 of her spit-taking. “It was just dribbling right down me. You have to learn how to direct it. It works better as a mist, but sometimes it comes out as Niagara Falls.”