Viola Davis also made history by becoming the first black woman to win the best lead actress prize for her role in How To Get Away With Murder.
Jon Hamm finally won a best actor award for Mad Men in the show’s last year. He had been nominated seven times before.
Political comedy Veep was the winner in the best comedy series category.
And Inside Amy Schumer was named best variety sketch series.
It was the first time since it began in 2011 that Game of Thrones had won the best drama series award. Its other accolades included best writing, best direction and best supporting actor for Peter Dinklage, who plays Tyrion Lannister.
Amazon’s comedy-drama Transparent won awards for best director in a comedy and for its lead actor, Jeffrey Tambor, who plays a transgender college professor.
The show also picked up best guest actor in a comedy for former West Wing star Bradley Whitford.
Viola Davis won her Emmy for lead actress in a drama thanks to 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.
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.
The show’s win for best comedy ended a fiver-year winning streak for sitcom Modern Family – dashing the cast’s hopes of beating Frasier, which also has five wins in the category.
Uzo Aduba, who plays Suzanne ‘Crazy Eyes’ Warren in Netflix prison series Orange is the New Black, was named best supporting actress in a drama.
The TV Academy awarded only four prizes to the main US broadcast networks. But while the pre-awards talk had revolved around streaming services such as Netflix and Amazon, it was cable channel HBO that swept the board, with shows like Veep, Game of Thrones and Olive Kitteridge performing well.
The latter picked up six awards, including best mini-series, best lead actor in a mini-series or movie (Richard Jenkins), lead actress (Frances McDormand) and supporting actor (Bill Murray).
Andy Samberg hosted the show, his first time at the helm of a major awards ceremony.
Variety’s Brian Lowry wasn’t overly impressed with Samberg’s debut: “What mostly came across, gradually, was that Samberg’s approach just didn’t wear especially well. He plays better in bite-sized bits, and his sprightly setup/joke rhythms yielded diminishing returns over the course of the evening.”
But USA Today reviewer Robert Bianco was a little more effusive.
“For most viewers, the show only works if the host works, and Samberg did just fine. Like all modern awards show hosts, he did throw a few jabs at some of the folks in the room, but they were generally mild, which is what the job requires.”