Baker was born in the Washington, D.C. area and attended Robert E. Lee High School in Fairfax County, Virginia. After graduating from James Madison University with a double major in Theater and English, she moved to Atlanta, Georgia. There, she helped build Whole World Improv Theatre as a performer, and later as a teacher. Moving to Los Angeles, she continued to hone her improvisational and sketch comedy skills at The Groundlings.
In 2012, Baker appeared as Mitzi Huggins, wife of Zach Galifianakis' congressional candidate, along with Will Ferrell, in the comedy The Campaign. In addition, she played Becky in Tammy, starring Melissa McCarthy, and directed by Ben Falcone. Baker has also appeared as Pamela Lowi in The Good Lie, about the Lost Boys of Sudan, which was directed by Philippe Falardeau(director of the Oscar-nominated Monsieur Lazhar).
Baker has also appeared as Vanessa on the FX show Louie. This performance was nominated for the Critics' Choice Television Award for Best Guest Performer in a Comedy Series. Additionally, Entertainment Weekly nominated the performance for one of their annual "EWwy Awards." The performance was included on numerous year-end "best of" lists for 2014, including NPR's "50 Wonderful Things from 2014".
She was also seen as Series Regular Sonia on the Matthew Perry sitcom, "Go On." Other TV appearances have included guest and recurring roles on shows such as A to Z, Bob's Burgers, Mike & Molly, Bones, The Crazy Ones, In the Motherhood, Kath & Kim, Modern Family, The Office, and more.