The hit comedy scooped awards for directing, make-up, costumes and hair, and made it five wins with Fallon named as best guest actor in a comedy.
Sherlock: His Last Vow, the final episode in the drama's third season, took four awards, for cinematography, music, single-camera picture editing, and sound editing.
Game Of Thrones also won four honours - for art direction, costumes, make-up, and special effects - as did True Detective (cinematography, make-up, title design, and casting) and the documentary Cosmos: A Spacetime Odyssey (theme music, composition, sound editing, and writing).
There were also awards for Allison Janney for guest actress in a drama for her role in Masters of Sex, and Joe Morton for guest actor in a drama for Scandal.
Downton Abbey, Orange is the New Black, and reality shows Shark Tank and Deadliest Catch also won honours at the ceremony in Los Angeles on Saturday (16Aug14).