Peters scooped the prize for Best Actor in a Limited or Anthology Series or Television Film for his lead performance in Ryan Murphy's show Dahmer – Monster: The Jeffrey Dahmer Story.
Read more: Most searched for streaming box sets of 2022
Dahmer murdered 17 men and boys between 1978 and 1991, standing as one of the most notorious serial killers in American history.
The series received a mixed critical response, and also got backlash from the families of some of Dahmer's victims for what they perceived as an insensitive approach to the subject matter.
Eric Perry, a relative of Dahmer victim Errol Lindsey, said the series was effectively "retraumatizing" the families and added: "I want people to understand this is not just a story or historical fact, these are real people’s lives."
Peters took to the stage at the Beverly Hilton on Tuesday night to accept his award and offered his gratitude to the viewers who made the series one of Netflix's biggest recent hits.
Read more: Full list of winners at Golden Globes 2023
He said: "Most importantly, I want to thank everyone out there who watched the show. It was a difficult one to make and a difficult one to watch, but I sincerely hope some good came out of it."
Viewers of the Golden Globes ceremony were not impressed though, particularly noting that Peters did not mention Dahmer's victims in his speech at all.
The experience of playing Dahmer clearly had an effect on Peters, who told Variety in December that he plans to "take a little break from darker roles and explore the light" in the wake of the series.
He added: "It would be interesting to me to play something that is a little closer to home, a little more mundane and to explore the details of those kinds of experiences."
In an interview with The Hollywood Reporter, he explained that the Will Ferrell and John C Reilly comedy movie Step Brothers helped him to de-stress after filming.
Following the success of the Dahmer series, Netflix renewed the "Monster" series as an anthology, with two further seasons based on "other monstrous figures".
Watch: Trailer for the Jeffrey Dahmer series on Netflix, starring Evan Peters