The show, which follows three branches of a quirky California family, also picked up the prizes for Supporting Actor and Actress, Directing and Writing.
"I don't know what I'm going to talk about in therapy next week now," Julie Bowen joked as she collected her Outstanding Supporting Actress in a Comedy Emmy. "I can't believe this."
"Thank you so much for this honor," Ty Burrell, Bowen's small-screen husband said as he accepted his matching Supporting Actor Emmy.
Melissa McCarthy won the award for Outstanding Lead Actress in a Comedy Series for her work in "Mike & Molly."
In addition to her statuette, McCarthy was also presented with a tiara and flowers.
"Holy smokes. This is my first and best pageant ever," she remarked.
Jim Parsons won the Emmy for Lead Actor for "The Big Bang Theory."
"Glee" star Jane Lynch served as host of the event.