The drama - screened on both ITV and TV3 - also saw actor David Bradley scoop an award for Best Supporting Actor.
The hotly-tipped Olivia Colman scooped the award for Lead Actress in the series.
The drama also starred David Tennent.
However, Tennent lost in the Lead Actor category to Sean Harris, who won for his role in 'Southcliffe'.
Coronation Street won the BAFTA TV award for Best Soap and Continuing Drama, beating rivals Eastenders.
BBC soap Eastenders has won the award for a number of years - but in recent years, critics have said that Coronation Street's storylines have proved far stronger than anything Albert Square have had to offer.
Other big winners so far at the BAFTA TV Awards include Ant McPartlin and Delcan Donnelly, who won for their ITV programme 'Saturday Night Takeaway'. The presenters beat Graham Norton to win the award. They also won a second award for Entertainment Performance Award.
ITV News won an award for their coverage of the Woolwich attacks in which soldier Lee Rigby was killed.
Davina McCall accepted an award for her series 'Lost Families', while former Coronation Street star Sarah Lancashire was named Best Supporting Actress in drama 'Last Tango in Halifax'.
Sir Sir David Attenborough won the Specialist Factual Award for Natural History Museum Alive 3D, while actor David Bradley won Best Supporting Actor for his role in 'Broadchurch'.
Graham Norton was to lose out again - this time to Sky's 'A League of Their Own' for Best Comedy. The programme is presented by James Corden.
Aaron Paul, who played Jesse in hit US drama 'Breaking Bad', accepted the BAFTA TV International Award for the series.