Fernandez was first shown a yellow card for dissent, then a second for a spectacularly late challenge that sent Cubarsi somersaulting.
After the full-time whistle, Paredes was involved in scraps with Rodri, Gavi and Borja Iglesias and team mate Nahuel Molina was seen throwing a punch at a passing Spain player too.
“Embarrassing, seeing that sort of stuff after the game has been played,” said BBC pundit Wayne Rooney. “Someone has been crowned World Cup champions. It is not good enough.
“Paredes is better than that. It doesn’t stop there. He keeps going and going.”
Argentina manager Lionel Scaloni attempted to defend his side’s performance through floods of tears at his post-match media conference, but could only admit the best team had won.
“Even though they were out-playing us until the 85th minute, I would love to know what would have happened had we still had 11 men on the pitch,” he said of Fernandez’s dismissal.
“We managed to go all the way to the end when the match was so open and it just couldn’t be. They deserved the victory, that is the reality.”
Argentina might have taken the World Cup final to extra time – the fifth of the past six to go that far – but that could not mask their inferiority.
“Argentina can have absolutely no complaints about what happened,” former England goalkeeper Joe Hart told BBC One. “Disgusting behaviour.
“I don’t think Rodri needed to get in their faces but you understand that after 120 minutes where you have been wound up and you thought you’ve been wronged, and the referee has been on your back.”