The female filmmaker also triumphed over Spielberg for the title of Best Director, while Zero Dark Thirty's Greig Fraser earned the Best Cinematographer honour.
All was not lost for Lincoln - the historical epic earned Daniel Day-Lewis Best Actor for his portrayal as the assassinated U.S. president, and Sally Field, who played his onscreen wife, Mary Todd, claimed the Best Supporting Actress prize.
Lincoln also landed the Best Screenplay honour for writer Tony Kushner.
Meanwhile, Rachel Weisz's performance in British drama The Deep Blue Sea earned her the Best Actress accolade, while Matthew McConaughey picked up the Best Supporting Actor prize, scoring double recognition for his turn as a prosecutor in black comedy Bernie and as a strip club owner in Magic Mike.
Tim Burton's Frankenweenie was named Best Animated Film, and German director Michael Haneke, who celebrated a big Best European Film win at the European Film Awards on Saturday (01Dec12) was honoured for Amour, which the New York pundits named Best Foreign Language Film.
The New York Film Critics Circle's top picks are considered to be among the best indicators of the Academy Awards in the run up to the Oscars.
It was Bigelow's second win for Best Film and Best Director - she won the same awards in 2009 for The Hurt Locker, and went on to claim gold in the same categories at the 2010 Oscars.
The New York Film Critics Circle honours will be presented during a ceremony in New York on 7 January (13).