Five Daughters looked at the family relationships and lifestyles of the five victims of Steve Wright, who was convicted of their murders in 2008.
The three-part programme won the Drama Serial award.
Philippa Lowthorpe, director, said: "We would like to dedicate this award to the women who lost their lives."
The judges gave this verdict on Five Daughters:
"This sensitive, skilfully acted dramatisation of an appalling true story made for ground-breaking television.
"By concentrating on the victims of this terrible crime, the drama succeeded in giving the five women back some dignity and humanity.
"Powerful and important, this is TV drama at its very best."
Writer Stephen Butchard was also nominated in the Writer-Drama category which was won by Jack Thorne and Shane Meadows for This Is England '86.
Gemma Adams, Tania Nicol, Anneli Alderton, Annette Nicholls and Paula Clennell had been working as prostitutes in the Ipswich area when they were murdered.
The writers, actors and producers spent a year researching the story with some of the victims' relatives, Suffolk police and the Ipswich drugs rehabilitation charity the Iceni Project.
Liz Harsant, the leader of Ipswich Borough Council and a trustee of the Somebody's Daughter Memorial Fund, said: "We met the actors and producers and all of them were touched by the stories the parents had told them.
"I can't say how pleased I am that they've won the award.
"It's not something you want to relive every day of your life, but I think people had to know about it."
Ms Lowthorpe added: "Our hope is that the drama continues to spark a debate about drug addiction and girls on the street, and for drug charities, like Iceni, to be supported to continue to do the tremendous work they do."
A BBC drama about the 2006 murders of five women who worked as prostitutes in Ipswich has won a Royal Television Society award.