Her recent storyline, in which she was attacked and raped by a visiting valet, led in part to her triumph and she paid tribute to those who had thanked her for addressing the issue.
"I received a small number of letters from survivors of rape," Froggatt said in her acceptance speech. "One woman summed up the thoughts of many by saying she wasn't sure why she'd written but she just felt in some way she wanted to be heard.
"I'd like to say, I heard you and I hope saying this so publicly in some way means you feel the world hears you."
Golden Globes 2015 winners
Show all 15
Some viewers complained when the scene in which Anna is raped was broadcast, with 60 people ringing ITV and more than 30 contacting TV watchdog Ofcom.
Writer Julian Fellowes defended the controversial plot and insisted that it had not been done "gratuitously" but to "explore the resultant emotions and the effect these things have on people".
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies