In 2012, Baker appeared as Mitzi Huggins, wife of Zach Galifianakis' congressional candidate, along with Will Ferrell, in the comedy The Campaign. The Jay Roach-directed film is the highest grossing politically themed movie of all time. In 2014, 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). In 2015, she appeared in Barry Levinson's Rock the Kasbah, alongside Bill Murray.

She 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. Entertainment Weekly included the performance in its "50 Best TV Scenes" of 2014, and later 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". This role later led to Baker's performance as Trinity on Pamela Adlon's Better Things in 2016, in an episode written by Adlon and Louis CK.

In 2016, she was in a number of films, including Christopher Guest's Mascots where she played Mindy Murray, aka Tammy the Turtle. Other movies released in 2016 include The Meddler, starring Susan Sarandon and directed by Lorene Scafaria, where Baker played Elaine. Baker also appeared opposite Shirley MacLaine in The Last Word and in the film adaptation of the acclaimed Speech & Debate, playing Ms. Riggi. In 2018, she will appear as Gildred in Melissa McCarthy's Life of the Party, and in Paul Feig's A Simple Favor.

On TV, Baker was also seen as series regular Sonia on the NBC comedy Go On, starring Matthew Perry, as a support group member dealing with the loss of her cat. In 2017, she played the recurring role of Thea Cunningham on HBO's limited series Big Little Lies, based on the popular book of the same name.

Other TV appearances have included guest and recurring roles on shows such as A to Z, Bob's Burgers, Bones, Brooklyn Nine-Nine, The Crazy Ones, Ghosted, Graves, Great News, In the Motherhood, Kath & Kim, Key & Peele, Mike & Molly, Modern Family, New Girl, The Office (U.S. version), The Santa Clarita Diet, Sean Saves the World, and more. In 2018, Baker appeared in the acclaimed "Kill All Others" episode of Philip K. Dick's Electric Dreams, alongside Mel Rodriguez. Baker appears in the DVD/Blu-ray bonus scenes of the hit comedy Bridesmaids, as a nurse arguing with an injured Paul Rudd. Online, she was seen as Arabella, faithful servant to Megan Mullally in the Funny or Die video Home for Actresses.