Fleabag’s creator and writer Phoebe Waller-Bridge took home the prize for best leading comedy actress and best writing for a comedy series, BBC reports.
“It’s so wonderful and reassuring to know that a dirty, pervy, angry and messed-up woman can make it to the Emmys,” she laughed, referring to the show’s lead character.
The actress also joked that the possibility of winning awards was the reason she wrote the series in the first place.
“I find writing really hard and really painful, but I’d like to say from the bottom of my heart that the reason that I do it is this,” she said, holding up the Emmy statuette. “So it’s made it all really worth it guys, thank you so much.”
The US actress has previously won in this category six times for her role in Veep, and was widely expected to win again for the show’s seventh and final series.
The show’s director, Harry Bradbeer, also won the prize for best director for a comedy series.
“I think for a director, something like Fleabag only comes along once in your life,” he said in his acceptance speech.
“Thank you Phoebe for coming into my life like some kind of glorious grenade. Scientists are still trying to work out how someone so incredibly talented can be so utterly lovely.”
Other British winners include Ben Whishaw, who won best supporting actor in a limited series for his role in A Very English Scandal.
The final season of Game of Thrones is among the other nominees at the ceremony.
The fantasy epic, which came to a divisive climax earlier this year, has 14 nominations in seven categories.
The 32 Emmy nominations Game of Thrones received in July was the highest total for any programme in a single year.
The show has already won 10 prizes at the Creative Arts Emmys held last weekend, including awards for its casting, costumes, make-up and music.
If Game of Thrones adds just three more awards to that tally on Sunday, it will better the 12 Emmys it received in both 2015 and 2016.
The show is already the most honoured series and most-nominated drama in Emmy awards history.
British stars in contention include Hugh Grant, who is nominated for best actor in a limited series or movie for A Very English Scandal.
Alfie Allen, meanwhile, is one of three Game of Thrones stars up for outstanding supporting actor in a drama, having put himself forward for a nomination earlier this year.
Sunday’s event – to be held at the Microsoft Theatre in downtown Los Angeles – will be only the fourth Emmy ceremony ever not to have a host.
More than 25,000 members of the Television Academy vote for the awards, which were first presented in 1949.
The name Emmy derives from an early piece of TV equipment called the image orthicon camera tube, nicknamed the Immy.