Williams was only player ejected during the melee in which players from both teams scuffled in the end zone after quarterback Cam Newton scored on a 2-yard dive to give the Panthers a 17-0 lead.
It began when Newton got into a shouting match with defensive end Cameron Jordan. He eventually -- in front of Jordan -- did his "Superman" taking flight celebration (a thrusting gesture that looks similar to one that a pro wrestler makes as he's putting on his championship belt), followed by the "Superman" ripping open his shirt celebration.
At that point, Newton was pushed in the back by linebacker Curtis Lofton while continuing to jaw with Jordan.
That's when Williams entered the picture, trying to pull players away from Newton. That eventually led to punches being thrown.
Carolina coach Ron Rivera defended Williams, saying if one player is thrown out then one from New Orleans that started the fight also should have been.
Williams said he plans to appeal the fine, his first. If he loses, he said he'll "take my punishment like a man, and hopefully not get another one."