The Indomitable Lions' task was soon tougher as Song was dismissed for lashing out at Mandzukic off the ball before the interval.
Having made the opener with a fine pass, Perisic scored a second three minutes into the second half after a fine solo run and Mandzukic headed in a third before tapping in a fourth to complete a comfortable win.
Croatia play Mexico next Monday with a place in the knockout stages at stake, while Cameroon are out ahead of their clash with Brazil.
Their frustrations appeared to boil over when Benoit Assou Ekotto and Benjamin Moukandjo had a dispute on the field, with the full-back perhaps fortunate to avoid a sending off for an apparent headbutt on his team-mate.
Cameroon were without talisman Samuel Eto'o due to a knee injury, while Croatia had striker Mandzukic available again following his suspension for his dismissal in the play-off with Iceland last November.
Cameroon were soon behind when they failed to clear Darijo Srna's cross towards Mandzukic.
Perisic had the composure to deliver a finely-weighted diagonal pass across the area for Olic to simply tap in.
Croatia took control of the contest and were given a numerical advantage when Song struck Mandzukic on the back as Croatia began an attack, with referee Pedro Proenca showing no hesitation in brandishing a red card.