YouTuber Paul, 26, laboured to a points win over UFC legend Diaz, 38, who was making his professional boxing debut.
But ugly scenes took place outside the ring as those watching the bout turned on one another and began brawling.
A video shared on social media showed multiple fights breaking out.
And people on Twitter were quick to condemn the violent actions of the fans.
One said: “Look at these thugs!”
Another added: “So embarrassing. Acting like savages.”
And a third replied: “A bunch of losers in life. None of these people do absolutely anything valuable with their life. No coincidence.”
Meanwhile, after beating Diaz, Paul said: “I knocked him down, won basically every round. I think he won one round but he’s a warrior.
“I had him hurt in the first round, he kept on coming. All credit to my team, my conditioning, going ten rounds in my eighth fight, it’s unheard of.
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“I’ve only been boxing for three years, he’s a UFC legend, I was watching this kid growing up.”
Paul had snubbed a rematch with Tommy Fury, 24, following his split-decision defeat in Saudi Arabia last February.
He instead chose to welcome Diaz over to the boxing ring after the MMA veteran walked out on the UFC.
And Paul secured his seventh professional win as he dropped the American in the fifth round on his way to a unanimous decision victory.