Zico got the opener in the 12th minute when he reacted first after Eder's fierce free-kick came back off the bar.
Falacao and Scorates dominated midfield, and Brazil made the game safe in the second half through goals from Seginho and Junior.
Diaz managed a last-minute consolation for Argentina, but their frustration was evident when Diego Maradona was sent off for kicking substitute Batista.
A draw against Italy would be enough to send Brazil into the semi-finals on goal difference, but this was not a side capable of playing for anything other than a win.
Played in the midday heat, the clash with Italy was one of the best in World Cup history.
Paolo Rossi ensured that Brazil made their customary poor start, heading Italy into the lead in the fifth minute.
Socrates came to the rescue just seven minutes later, latching on to a Zico pass and slipping the ball between Dino Zoff and the near post.
But the defensive frailties would not go away, and in the 25th minute Cerezo gave the ball straight to Rossi, who finished clinically.