The show, based on George RR Martin’s novels, has now scooped 38 Emmys, beating Frasier’s record of 37 to become the most-awarded narrative show in Emmy history.
Downton Abbey actress Dame Maggie stayed away from the Los Angeles ceremony but won a best supporting actress gong for her role as Violet Crawley, Dowager Countess of Grantham, in the hit period drama.
Her rivals included Game Of Thrones stars Lena Headey, Emilia Clarke and Maisie Williams, but the 81-year-old went on to land another Emmy to her bulging trophy cabinet - her third for her Downton role alone.
Host Jimmy Kimmel joked during his opening monologue that the veteran actress should have made an effort to be at the event, having not attended in previous years either.
“If you want an Emmy you better hop on a plane right now and get your Dowager Count-ass over here,” he joked.
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When her name was announced as winner, he walked on to the stage to take Dame Maggie’s trophy, saying: “No, no, no, no, no. We’re not mailing this to her. Maggie, if you want this, it’ll be in the lost and found.”
British comedian John Oliver, who made his name on The Daily Show with Jon Stewart, won outstanding variety talk show for satirical programme Last Week Tonight.
He beat big names including James Corden, Kimmel and Jimmy Fallon to the gong.
Sherlock: The Abominable Bride, the much-anticipated Victorian era-set special featuring Benedict Cumberbatch and Martin Freeman, which left some viewers puzzled when it was broadcast on New Year’s Day, received the television movie award.
Cumberbatch had been nominated for his acting role in the special, but went away empty-handed.
Sherlock writer Steven Moffat brought The Great British Bake Off controversy to a US audience when he received the award, saying: “Thank you to the BBC, who we love above all bakery. British people will get that.”
Tom Hiddleston left without an award after being nominated for his role in The Night Manager, the thriller based on the John le Carre novel.
But the British-US miniseries did scoop a directing gong, for Danish filmmaker Susanne Bier.
Sky Atlantic fantasy Game Of Thrones was named best drama series and picked up gongs for outstanding writing and directing at the event in Los Angeles, although there was disappointment for British heartthrob Kit Harington as well as Headey, Clarke and Williams.
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The TV drama based on the murder trial of OJ Simpson, The People v OJ Simpson: American Crime Story, was also honoured with a host of acting awards and was named outstanding limited series.
Julia Louis-Dreyfus won an Emmy for her role in the political satire Veep, which was named best comedy series, and paid a heartfelt tribute to her father following his death on Friday.
The US star fought back tears as she collected the outstanding lead actress in a comedy series award, saying: “I’m so glad that he liked Veep because his opinion was the one that really mattered.”
It is the fifth time in a row Louis-Dreyfus has won the award for her role in the US version of BBC comedy The Thick Of It.
Jeffrey Tambor won best lead actor in a comedy series for his role in the Amazon series Transparent and urged the TV industry to provide more opportunities for transgender actors.
“Please give transgender talent a chance,” he said. “Give them auditions. Give them their stories.”
Rami Malek was named best lead actor in a drama series for his role in Mr Robot, while Tatiana Maslany won best actress in a drama series for her performance in BBC America series Orphan Black.
The 68th Emmy Awards took place at the Microsoft Theatre in Los Angeles.