Ivica Olic scored just 11 minutes into the affair to put Niko Kovac's men in front, but the match really turned in Croatia's favor five minutes before halftime when Alex Song was issued a straight red card.
The extra man helped Croatia dominate the second half as a goal from Ivan Perisic and a brace from Mario Mandzukic wrapped up the comfortable win.
Croatia, which was without Mandzukic for its opening defeat to Brazil last week, wasted little time getting off the mark, and it was the Bayern Munich man that helped create the chance.
Mandzukic made a near-post run in the 11th minute to open up space at the back post for Olic. Perisic recognized the move and slid a pass across the face of goal for the Wolfsburg striker to tuck home from close range.
The Croatians continued to push in search of more goals and struggled to break through, but Song's dismissal for a punch to the back of Mandzukic gave them a massive boost, which they capitalized upon after the halftime interval.
Perisic doubled Croatia's advantage just three minutes into the second half, breaking free on the left flank before feigning a low cross to draw goalkeeper Charles Itandje out of position and slotting a shot into the back of the net.
Mandzukic then put the icing on the cake by scoring twice inside the final half-hour.
The first came in the 61st minute when he nodded home following a corner kick.
The Bayern striker then completed his brace 12 minutes later, turning in a rebound conceded by Itandje.
The result sees Croatia improve to three points in Group A to set up a tantalizing meeting with Mexico at the Arena Pernambuco on Monday.
Cameroon, still searching for its first goal in the 2014 World Cup, will attempt to rebound on Monday when it faces Brazil at the Estadio Nacional.