The police drama, filmed in the Halifax and Hebden Bridge area, starring Sarah Lancashire snatched the best drama series prize from the big budget Netflix production, while Lancashire took the leading actress prize over The Crown's star Claire Foy.
Addressing the tearful actress, who played a young Queen Elizabeth II in the series, Lancashire said: "Claire Foy, you have given me the best 10 hours under a duvet that I have ever had, thank you."
The Crown also missed out on the best supporting actor gong, despite both Jared Harris and John Lithgow being nominated.
The prize instead went to The Night Manager star Tom Hollander, while the supporting actress prize went to Wunmi Mosaku for Damilola, Our Loved Boy over The Crown's Vanessa Kirby.
Before the ceremony at the Royal Festival Hall, nominees were warned acceptance speeches would be cut short if they became too political and jeopardised the BBC's impartiality rules ahead of the General Election.
That did not stop host Sue Perkins poking fun at Theresa May, as she said: "I promise to deliver you a strong and stable Baftas."
Ant & Dec had a successful night as the live event prize was won by The Queen's 90th Birthday Celebration, which they fronted on ITV, while Ant & Dec's Saturday Night Takeaway won the entertainment prize.
It was also a winning night for the BBC's nature series Planet Earth II, which won the specialist factual Bafta, although narrator Sir David Attenborough did not join the production team to collect the prize.
It also claimed Virgin TV's must-see moment prize for the snakes versus iguana chase.
Collecting the gong, executive producer Mike Gunton said: "We are surprised this won because half of people watched this sequence from behind their sofa, but the other half were at home shouting 'run iguana run' and they must be the ones who voted."
Damilola, Our Loved Boy, about the killing of schoolboy Damilola Taylor, won the Bafta for single drama, while the mini series prize was taken by National Treasure, a drama inspired by Operation Yewtree.
Who Do You Think You Are? triumphed over The Great British Bake Off for the features prize while People Just Do Nothing beat Fleabag, Flowers and Camping for the scripted comedy gong.
The female performance in a comedy programme prize was taken by Fleabag star Phoebe Waller-Bridge, beating her co-star Olivia Colman.
Nick Fraser was presented with the Bafta special award for his 20 years as editor of the BBC's Storyville documentary strand.
Fraser, who suffered a stroke earlier this year, stood next to his daughter Isabelle, as she read out his speech.
Hillsborough, a programme about the 1989 football tragedy, won the single documentary prize.
The Bafta Fellowship was presented to Joanna Lumley by her Absolutely Fabulous co-star Jennifer Saunders, who said: "In 1990 I handed her some scrappy lines and unformed ideas and she alone created Patsy Stone, a creation that has at least kept me laughing for 27 years.
"She's a comic genius and a brilliant clown who never forgets how hard it's been to get where she is."
Lumley said it was "paradise" to receive the honour before she adopted Patsy's famous drawl to add: "I just want to say actually to you all, thanks sweeties, thanks a lot."
Emmerdale took home the award for best Soap and Continuing Drama, beating the likes of Eastenders and Coronation Street.
Here is a list of winners:
Comedy & Comedy Entertainment Programme
Charlie Brooker's 2016 Wipe Production Team - House of Tomorrow/BBC2
Teenage Prison Abuse Exposed (Panorama) Production Team - BBC Productions/BBC1
Happy Valley Sally Wainwright, Juliet Charlesworth, Nicola Shindler, Neasa Hardiman - Red Production Company/BBC One
Michael McIntyre, Michael McIntyre's Big Show - Hungry McBear/BBC1
Ant & Dec's Saturday Night Takeaway Production Team - ITV Studios/Mitre Television/ITV
Exodus: Our Journey To Europe Production Team - Keo Films/The Open University/BBC Two
Who Do You Think You Are? Colette Flight, Sarah Feltes, Anna Kirkwood, Helen Nixon - Wall to Wall Media/BBC1
Female Performance In A Comedy Programme
Phoebe Waller-Bridge, Fleabag - Two Brothers Pictures/BBC Three
The People V OJ Simpson: American Crime Story Ryan Murphy, Nina Jacobson, Brad Simpson - Fox 21 Television Studios/Fx Productions/BBC Two
Adeel Akhtar, Murdered By My Father - BBC Studios/BBC3
Sarah Lancashire, Happy Valley - Red Production Company/BBC1
The Queen's 90th Birthday Celebration Production Team - ITV Studios/Spun Gold Television/ITV
Male Performance In A Comedy Programme
Steve Coogan, Alan Partridge's Scissored Isle - Baby Cow Productions/Sky Atlantic
National Treasure George Ormond, Marc Munden, Jack Thorne, John Chapman - The Forge/Channel 4
Victoria Derbyshire: Footballers' Abuse Victoria Derbyshire, Louisa Compton, Jo Adnitt - BBC News/BBC2
Reality & Constructed Factual
Muslims Like Us Kieran Smith, Nicholas Packer, Oliver Manley, Mobeen Azhar - Love Productions/BBC2
People Just Do Nothing Production Team - Roughcut TV/BBC Three
Hillsborough Production Team - Very Much So Productions/Passion Pictures/BBC Two
Damilola, Our Loved Boy Levi David Addai, Euros Lyn, Susan Horth, Colin Barr - Minnow Films/BBC1
Soap & Continuing Drama
Emmerdale Production Team - ITV Studios/ITV
Planet Earth II Michael Gunton, Tom Hugh-Jones, Elizabeth White, Sir David Attenborough - BBC Studios/BBC Natural History Unit/BBC America/Zdf/France Television/BBC One
The Open Production Team - Sky Sports/European Tour Productions/Sky Sports 1
Tom Hollander, The Night Manager - The Ink Factory/Demarest/Character Seven/BBC1
Wunmi Mosaku, Damilola, Our Loved Boy - Minnow Films/BBC1
Virgin TV's Must-See Moment
Planet Earth II: Snakes Vs Iguana Chase - BBC Studios/BBC Natural History Unit/BBC America/ZDF/France Television/BBC1