On television, she played Sofie in Carnivà le (2003–2005), Audrey Hanson in Heroes (2006–2007), Wendy Peyser in American Horror Story: Asylum (2012–2013), Emma Borden in The Lizzie Borden Chronicles (2015), Lara Cruz in Better Call Saul (2015–2017), Marjorie in Veep (2016–2019), and Sylvia in The Handmaid's Tale (2018–2022).
In 2016, DuVall made her feature directorial debut with The Intervention, which she also wrote and co-produced. Her next project as director was Happiest Season in 2020.
DuVall was born in Los Angeles, California. Her father, Steph DuVall, is also an actor. Her forename derives from the novel Clea by Lawrence Durrell. She once worked in a coffee shop and studied at the Los Angeles County High School for the Arts.