11:57 AM PT -- A spokesperson from the Arizona Department of Public Safety tells TMZ Sports ... the fracas all began after two women pushed each other.

"One female fell down," the rep said. "A male friend ran after the suspect ... brushing by other males before a fight ensued."

The spokesperson added three men were ultimately arrested for misdemeanor assault.

Several Arizona Cardinals fans whaled on each other in the stands of the team's game Sunday afternoon ... and things turned so violent -- one guy actually left the area leaking blood.

It all went down in the upper deck of State Farm Stadium as the home team was taking on the Washington Commanders ... when for some reason -- a whole bunch of Cards supporters turned on each other.

You can see in video captured by a fan seated a few rows away from the action ... after a dispute turned physical, a guy in a Pat Tillman jersey got socked in the face repeatedly.

Following several big blows, the combatants got in a bit of a wrestling match -- yet once authorities arrived on scene, things appeared to calm down.

But just as the Tillman fan began leaving the scene, another man appeared to come out of nowhere .... and fired off yet another haymaker.

Cops eventually wrestled the man to the ground and put him in handcuffs. Seconds later, the Tillman fan seemed to book it from the area.

No word yet if anyone was actually arrested -- we've reached out to law enforcement, but haven't heard back yet.

The fight, of course, was hardly the only one around the NFL on Sunday ... just hours earlier, some Falcons fans got in some scary brawls in Atlanta as well.