Actress Laura Benanti isn’t a household name — beyond live theater, recent credits include a role as a troubled country singer on “Nashville” and “Supergirl’s” mom on the CBS show. But her appearance on Tuesday’s “The Late Show” might change that.

In a skit mocking the plagiarism scandal surrounding aspiring first lady Melania Trump, host Stephen Colbert introduced the politician’s wife and invited her to make some remarks. Benanti, who has previously discussed her resemblance to the former model, appeared behind a podium, wearing a replica of Melania Trump’s bell-sleeved sheath. Benanti, a Broadway mainstay, delivered well-known lines, from “The Fresh Prince of Bel Air” to Dr. Seuss. The lip-pursing, cautious movements and Eastern European accent were dead-on.

Looking like — and being able to give a comedic, yet faithful, impersonation of a political figure in a closely watched election — can prove very good for one’s career.

Take Tina Fey, who captured former vice-presidential candidate Sarah Palin in perfect send-up fashion on “Saturday Night Live.” She was already a well-known quantity, but her Palin impression is widely credited with boosting her fame. Fey, though, offered a word of caution about politician impersonations.

“Some may argue that exploiting Governor Palin and her family helped bring attention to my low-rated TV show,” Fey wrote in her memoir, “Bossypants,” of her NBC sitcom “30 Rock.” “I am proud to say you are wrong. My TV show still enjoys very low ratings. In fact, I think the Palin stuff may have hurt the TV show.”