Born during the silent era and perfected by Alfred Hitchcock, the cat-and-mouse crime thriller is practically as old as cinema itself. It has also become a staple of television in the binge-viewing age, in addictive series like “Fargo,” “Mindhunter” and “Narcos.”

BBC America’s sleeper hit “Killing Eve,” which ends its first season Sunday at 8 p.m., is part of this trend — but you need only glance at its credits to get an idea of what distinguishes it from its peers.

Based on a series of stories by Luke Jennings, “Killing Eve” follows the underachieving British intelligence agent Eve Polastri (the “Grey’s Anatomy” alum Sandra Oh, also an associate producer) as she tracks a glamorous, young female assassin known as Villanelle (Jodie Comer) across Europe. Spy thrillers almost never cast women as both the cat and the mouse, and this one also features an equally rare female presence behind the camera: The English writer and actress Phoebe Waller-Bridge, who created and starred in the pitch-black comedy “Fleabag,” is the series’s lead writer, showrunner and executive producer.

Ms. Waller-Bridge realized early on that Eve and Villanelle were more than just hero and villain; they were two broken women whose flaws bound them together in a twisted pas de deux. “Female obsession with other females is rife,” she said recently. “I’ve been obsessed with too many women — way more than I have been with men.”