Brown impersonated Robert and mentioned how the conservationist talked her into holding a snake.
The actress said she spoke to Robert about getting tortoises as pets, finally deciding to take home two of them.
Brown performed Winehouse's "You Know I'm No Good" after Fallon shared footage of the Stranger Things star singing Winehouse's "Valerie" at the age of 5.
Brown and Fallon then took part in a game of Beat Battle where they took turns singing as many songs as they could think of to go along with a beat played by The Roots.
Brown performed songs such as "Call Me Maybe" by Carly Rae Jepsen, "Juice" by Lizzo and "Royals" by Lorde, among others.