Play video content EXCLUSIVE

Bristol Palin hysterically told cops during the epic drunken Palin family brawl in Alaska last month ... that some guy knocked her down and called her a f**king c**t.

Bristol's conversation with cops outside the party near Anchorage was recorded by the officer and TMZ obtained a copy. During the convo ... Bristol explains the fight was triggered by an "old lady" who shoved her younger sister, Willow.

Listen carefully ... you can hear Sarah Palin in the background telling Bristol not to cuss during her statement.