The fantasy show won best drama series among other categories, while Viola Davis became the first black woman to win the lead actress prize for her role in How To Get Away With Murder.
Jon Hamm won lead actor for his role as Don Draper in Mad Men after he was previously nominated seven times.
Political comedy Veep was the winner in the best comedy series category.
Game of Thrones won best drama series for the first time in the five years it has been on air, along with awards for writing, directing and supporting actor Peter Dinklage, who plays Tyrion Lannister.
In the first Emmys for Amazon.com's foray into original content, Transparent won awards for best director in a comedy and for its lead actor in a comedy, Jeffrey Tambor.
Transparent, a comedy drama, is about a man transitioning to life as a woman.
Viola Davis won her Emmy for lead actress in a drama for her role as a tough criminal defence lawyer in ABC's How to Get Away With Murder.
Accepting her award, she said: "The only thing that separates women of colour from anyone else is opportunity.
"You cannot win Emmys with roles that are simply not there.'"
Jon Hamm, who played Don Draper in the drama Mad Men, set in an advertising agency primarily in the 1960s, said: "It's incredible and impossible for me personally to be standing here."
Julia Louis-Dreyfus won best comedy actress for the fourth time for playing Selina Meyer on Veep, while Tony Hale, who plays her bag man, was again named best comedy supporting actor.
Veep, which is set in the office of the fictional vice-president and subsequent president of the United States, Selina Meyer, also won the comedy writing statuette.
BBC