She took the prizes for breakthrough and best comedy writer for her BBC Three series Fleabag.
The show's success at the ceremony comes in the same week it was announced it had been renewed for a second season.
Other winners at Tuesday night's ceremony included Julie Walters, who won the Lifetime Achievement award.
"I simply can't thank all the amazing people I have elbowed out of the way to get where I am," the actress joked as she collected her prize.
Channel 4 picked up nine awards, including best actor for Robbie Coltrane's performance in National Treasure.
And Adam Hills, Alex Brooker and Josh Widdicombe took home the entertainment performance award for The Last Leg.
Elsewhere, ITV's Emmerdale won best soap while Ant and Dec's Saturday Night Takeaway won in the entertainment category.
The pair revealed their dream guest for the show - currently airing its 14th season - would be Adele.
"We've never quite made it work because of all her tours and albums and stuff, but we could have a lot of fun with her," the duo said.
"If you all put the pressure on from your end and we put the pressure on from our end, maybe we can make it happen."
Fleabag wasn't BBC Three's only success of the night - People Just Do Nothing won best scripted comedy for while best single drama was awarded to Murdered By My Father.
The network, which moved online last year, also took home channel of the year.
Happy Valley picked up the award for best drama series while the show's writer Sally Wainwright collected the best drama writer prize.
The Great British Bake Off was the hot topic of conversation backstage at the ceremony, which was held at London's Grosvenor House Hotel.
The new series of the show, being broadcast on Channel 4, will be fronted by Sandi Toksvig and Noel Fielding, with Prue Leith and Paul Hollywood serving as judges.
Hills, who presents The Last Leg, said: "The thing with TV is that you never know what's going to work."
"You could come up with something that seems logical for Bake Off and then nobody watches it, so you may as well take a punt on people like Noel and Sandi."
Responding to media coverage about Fielding, he added: "I'm surprised that the tabloids are trying to unearth stuff about Noel because he's bonkers - what did they expect his private life (was) going to be?
"He has told me stories that I cannot wait to hit the news, but I will let him share those."
Julie Walters told the Press Association: "I love Bake Off and I am so sad it has gone from the BBC, but I will definitely be watching the next series.
"I love Sandi and it will be very interesting to see how it transfers. It will just be a different experience from Mary Berry and maybe that will be good - who's to say?"
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.
Phoebe Waller-Bridge has scooped two prizes at this year's Royal Television Society (RTS) Awards.