The crazy fight began in the parking lot area of SoFi Stadium following the Cowboys' win over the Chargers ... when two women got into a heated argument.

You can see in the footage -- the two screamed at each other ... and then nearly came to blows.

As the scuffle was escalating, though ... one Cowboys fan screamed to a man trying to break up the tiff to "control your bitch."

That's when the L.A. supporter lost it -- calling the man a bitch as well, before charging at him and yelling, "F*** you!"

Complete chaos then ensued ... with several Cowboys fans rushing the man and whaling on him.

At one point, you can see in the clip, a man in a Troy Aikman jersey brutally tagged the Chargers fan in the face with a flurry of punches.

Eventually, the combatants separated ... and witnesses tell us the aftermath was bad, with blood all over one car -- while another car's side mirror was busted.

We're also told despite bystanders calling for cops and security ... nobody showed up until the fight was long over.

The brawl was far from the only altercation at the stadium following Dallas' big win ... with one scrap escalating so heavily, it ended up with people inside the stadium's water feature.