The Amazon Prime Video series, a drama about a group of vigilante superheroes, also saw Starr win the best villain in a series prize, while the programme was named best superhero series.
"Birds of Prey: And the Fantabulous Emancipation of One Harley Quinn" saw Ewan McGregor and Margot Robbie named best actor and actress in a superhero movie respectively, while Spike Lee's "Da 5 Bloods" won best action movie and best actor in an action movie for Delroy Lindo.
Elisabeth Moss was named best actress in a horror movie for her turn in "The Invisible Man", which also took home the best horror movie prize, while Vince Vaughn's role in "Freaky" saw him nab the best actor in a horror movie honour.
Patrick Stewart was named best actor in a science fiction/fantasy series for his portrayal of Jean-Luc Picard in "Star Trek: Picard", while Natasia Demetriou took home the best actress prize in that genre for "What We Do in the Shadows".
Other winners on the evening included Jim Carrey, who was named best villain for his role in "Sonic the Hedgehog", and Daveed Diggs, who won the best actor in an action series award for "Snowpiercer".
The full list of winners at the Critics Choice Super Awards is as follows: