Actor Peter Dinklage won outstanding supporting actor in a drama series and the show also picked up the prestigious outstanding drama series award.
Dinklage embraced co-star Lena Headey and told the packed crowd: "I was chewing gum, I wasn't prepared because the other actors in my category awe me with their performances."
The show also won outstanding directing for a drama series (David Nutter, Mother's Mercy) and outstanding writing for a drama series (David Benioff and D.B.Weiss).
It was an otherwise disappointing night for British TV talent, as shows like Downton Abbey walked away empty-handed.
Despite being nominated for three awards, among them supporting actor and actress in a drama series, the night belonged instead to American shows, Veep and Olive Kitteridge.
Success was also sweet for How To Get Away With Murder's Viola Davis and Mad Men star Jon Hamm.
Davis made Emmy history by becoming the first black actress to win the outstanding lead actress in a drama series award.
She quoted 19th century African-American abolitionist Harriet Tubman, saying: "In my mind, I see a line. And over that line I see green fields and lovely flowers and beautiful white women with their arms stretched out to me over that line.
"But I can't seem to get there no how. I can't seem to get over that line."
Davis said: "The only thing that separates women of colour from anyone is opportunity. You cannot win Emmys for roles that are not there."
Hamm finally scored the Emmy for outstanding lead actor in a drama series after seven previous nominations for the hit show and tripped over on his way up to the stage.
Composing himself and collecting his Emmy from Tina Fey, he said: "There has been a terrible mistake clearly. It is impossible to named with all those extraordinary gentlemen, it's impossible to be up here and to have done this show with these incredible people.
"It's incredible and impossible for me personally to be standing here so I want to thank the people I owe an incredible debt, families who have chosen for some reason to take me in and be nice to me.
"Thank you to everybody who watched the show and thank you for this."
British writers Armando Iannucci, Simon Blackwell and Tony Roche were awarded outstanding writing for a comedy series for their script for the election night episode of the political comedy, Veep.
It was also named outstanding comedy series in the penultimate award of the night.
Collecting the gong, creator Iannucci said: "If Veep is about one thing it's about hope, hope that anyone in America, no matter their background, their race, their creed, can just miss out on getting the top job. Or they can get it if their boss is mentally incapacitated or killed.
"So with that air of positivity, America has been so welcoming to the Brits on this show, thank you.
The show also saw Tony Hale presented with the Emmy for outstanding supporting actor in a comedy series, while Julia Louis-Dreyfus poked fun at the American presidential race as she scored the outstanding lead actress in a comedy series award for her role as President Selina Meyer.
Another big winner from the evening was Olive Kitteridge, which took home a host of awards, among them Bill Murray being named as best supporting actor in a limited series.
Emmy winners Louis-Dreyfus and Allison Janney arrived in the press room backstage holding hands, with Janney declaring: "We are going to throw down somewhere. We will play some cards."
Ianucci, who left Veep after the end of the last season, told the Press Association that the Emmy win for outstanding comedy series had not made him reconsider his departure.
Referencing Flavia Pennetta's surprising win at the US Open just before she announced her retirement, Ianucci said: "Like Italian tennis players who bow out when they win the Open, I am pleased to pass it on. It feels like the right time, every show can benefit from new ideas."
He attributed the win to the higher stakes in the fourth season of the show:
"We just get better with every season and now she's President, everything she does has terrible international consequences and that made everyone raise their game."
Amy Schumer told the assembled press it was a rollercoaster moment when her win for best variety sketch series was announced.
"I think you know how I'll be celebrating tonight," she said.
"When I won I just thought, I can't wait to hug my sister, and that was the first thing I did and I was sitting in a separate spot from the writers because I'm newly famous and so it was so exciting to see them all on stage and just be like, wow you're such a group of dirtbags. It's really fun to work here. And just being so proud of everybody. And I'm going to black out."
Hamm was greeted with applause from the assembled press as he arrived backstage.
Referring to his acceptance speech, he said: "I felt like saying a lot of things, I was honestly very surprised and I don't remember anything I said.
"It was a very odd experience because after I made my hilarious joke of climbing on to the stage the way I did I realised people were clapping for me.
"Over the many years we have been here, this is the culmination of this wonderful feeling."
Hamm said people still stop him in the street to discuss Don Draper with him.
"People want to talk about the show a lot to me and I always enjoy I unless I'm late to be somewhere.
"Our show was concurrent with the rise of TV blog culture and TV recaps and it's been an amazing thing to watch people put time into appreciating the show. I turned around on stage and saw all those people and was surprised and it was lovely."
Hamm was nominated seven times without success before taking home the Emmy this morning but he said he held no resentment for the times he lost.
"There are so many incredible people and incredible performances that have been honoured over my own. I can't hold a grudge at all, it's not like they gave it to some guy on the street.
"There is no animosity or anything like that, I have nothing to compare it to so year in and year out I'm just glad to be here and those are people I would watch if I wasn't an actor, these are people whose work I tremendously respect."
Davis said she would be celebrating her historic win with some indulgences: "Eating bread and dessert. You know if you eat bread in Hollywood, you're subversive? And drinking one, two, three, four drinks."
Asked about making history at the ceremony, she said: "I just feel like there is so much work that needs to be done in so many areas in the business with actors of colour, so many narratives that need to be seen by people, so many stories that need to be seen and felt, that I hope that it doesn't end here."
She added: "If it's been 67 years since and actress of colour has won an Emmy, then there's certainly been a line and it needs to be acknowledged just like the emperor being naked in the room."
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