"I can't help but compare my character to you, to a powerful, fearless woman that allows their expert work to stand before them," said Chastain after receiving the award for her portrayal of CIA agent Maya, who dedicates her life to hunting Osama bin Laden in Bigelow's movie, Zero Dark Thirty.
Bigelow may not have set out to break gender rules with 'macho-themed' movies, such as the iconic surfer-cop tale Point Break, the real-life naval account K-19: The Widowmaker, and the Iraq-based bomb disposal tale The Hurt Locker (for which she became the first female to receive an Oscar for directing), but as Chastain observed, she's successfully managed to "disobey the conventions of Hollywood".
"What's interesting to me is the topicality of something," says Bigelow, who at 61 looks incredible. "Certainly with The Hurt Locker and Zero Dark Thirty, there's an urgency, a resonance and a topicality that, as a filmmaker, makes it very stimulating and exciting material to work with."
Following the terrorist attacks on September 11, 2001, the hunt for Osama bin Laden preoccupied the world for more than a decade.
In the end, it took a small, dedicated team of CIA operatives to track him down to a compound in Abbottabad, Pakistan.
"It's the story of finding a very sharp needle in a very large haystack. Once bin Laden escaped from Afghanistan, he fenced himself in with a byzantine network that took years and years to unravel," Bigelow notes.
Every aspect of the mission was shrouded in secrecy and, while some details have been made public, many of the significant parts are brought to the screen for the first time in Zero Dark Thirty (the military code for the time -- 12.30am -- when the Navy SEALS stepped into bin Laden's hiding place).
Bigelow says: "The war on terror has touched everybody around the world, especially the families of 9/11 and first responders and military intelligence professionals, and it was a real honour to tell a story of that long, dark decade between 9/11 and May 1, 2011 (the date on which bin Laden was killed by the SEALS)."
The greatest creative challenge posed to Bigelow and Mark Boal -- the journalist-turned-screenwriter and producer of both this movie and The Hurt Locker -- was how to tell the multi-faceted story.
"That was tricky because you've got masses of information and you're compressing it into two-and-a-half hours," says California-born Bigelow.
The project began as a film about the failure to capture bin Laden in Tora Bora; the crew was in pre-production when they heard that bin Laden had been killed. Boal, who's been Bafta and Oscar nominated for his screenplay, had to start again.
"The public knows very little about what the unsung heroes in the intelligence community go through, which is as it has to be, but here you get a rare opportunity to have a first-hand look at the men and women at the heart of one of the most covert operations in our history," says Bigelow.
That's primarily achieved through the experiences of Maya who metamorphoses from a shell-shocked new recruit to steely navigator.
She's plunged into the hunt for bin Laden by witnessing the unsettling experience of an "enhanced interrogation" with a detainee.
The controversial scenes -- which depict the use of the torture technique waterboarding during the early stages of the hunt -- sparked global debate.
"As a human I wanted to cover my eyes, but as a filmmaker, I felt a responsibility to document and bear witness," she says.
But if she ever felt overwhelmed by what she'd undertaken, she isn't one to admit it, adding: "Actually I was just so honoured to tell this story. I think of it as a story of a lifetime."
Zero Dark Thirty has been nominated for five Oscars, including Best Picture, but Bigelow isn't in the running for Best Director. Does she feel snubbed?
"There's such an outpouring of excitement for it, so that's what's incredibly gratifying," she says.