"This is so much good fortune it's almost too much to bear," said Louis-Dreyfus. "I'm very grateful to have the opportunity to make people laugh. It's a joyful way to make a living."
Parsons added to the awards he won in 2011 and 2010 for the role of a science nerd.
"My heart, oh my heart. I want you to know I'm very aware of how exceedingly fortunate I am," he said.
Merritt Wever of "Nurse Jackie" won the night's first award, for best supporting actress in a comedy series, kicking off the ceremony on a surprising note and with a remarkably brief acceptance speech.
"Thank you so much. Thank you so much. Um, I got to go, bye," Wever told the audience after besting a field that included two-time winner Julie Bowen of "Modern Family."
"Merritt Wever, best speech ever," host Neil Patrick Harris said.
Backstage, she offered an explanation: "I'm sorry I didn't thank anyone. I was going to cry."
Tony Hale of "Veep" claimed the trophy for best supporting actor in a comedy, a category that has been the property in recent years of the men of "Modern Family."
"Oh, man.... This is mindblowing, mindblowing," Hale said.
Laura Linney was named best actress in a miniseries or movie for "The Big C: Hereafter." ''The Voice" won best reality-competition program, and Tina Fey won for writing "30 Rock."
Michael Douglas was honored as best actor for his portrayal of Liberace in "Behind the Candelabra," besting his co-star Matt Damon. The film also captured a top trophy as best movie or miniseries.
"This is a two-hander and Matt, you're only as good as your other hand," Douglas said, then got really racy: "You want the bottom or the top?"