Glazer, who was raised in Barnet, London, said it was an "honour" to win the award - the UK's first win for the category.
The German-language film, which earned a total of five Oscar nominations, focuses on the family of Auschwitz's longest-serving commandant, Rudolf Höss.
Höss ran the Auschwitz concentration camp between 1940 and 1943. An estimated 1.1 million people were murdered there - one million of whom were Jews.
After thanking those who worked with him on the film, Glazer - reading from a pre-written speech - said: "All our choices were made to reflect and confront us in the present, not to say look what they did then, rather what we do now.
"Our film shows where dehumanisation leads at its worst. It's shaped all of our past and present."
The director, who is Jewish, added: "Right now, we stand here as men who refute their Jewishness and the Holocaust being hijacked by an occupation which has led to conflict for so many innocent people.
"Whether the victims of October 7th in Israel, or the ongoing attack on Gaza, all the victims of this dehumanisation, how do we resist?"
Meanwhile Oppenheimer was a big winner, taking home seven awards – including best picture, best actor and best director.
Christopher Nolan’s blockbuster biopic about the Jewish theoretical physicist known as the “father of the atomic bomb”, J Robert Oppenheimer, took home seven Oscars after being nominated in 13 categories.
Earlier this year the film, starring Irish actor Cillian Murphy, was victorious at the Golden Globes and Critics Choice Awards.
Cillian Murphy was named best actor for his performance and Robert Downey Jr was named best supporting actor.
On collecting his first nomination Murphy said: “I’m a little overwhelmed.”
The actor dedicating his award “to the peacemakers everywhere”.
