Mario Mandzukic scored a brace in his team's much-needed win in the tournament after the 1-3 loss to hosts Brazil and the photo leakage controversy in the media.
Ivica Olic (11th minute) and Ivan Perisic (48th minute) scored the other two goals in a match that had promised many more.
Mandzukic did not play Croatia's opening match and chipped in when it was needed the most in today's game. He headed in a corner in the 61st minute while scored from a rebound in the 73rd minute.
Cameroon, missing the service of their best man Samuel Eto'o, were reduced to 10 men after midfielder Alex Song was shown the red card in the 40th minute for elbowing Mendzukic from behind even when the ball was not for taking.
Croatia now have three points from two matches and are placed third in the group after Brazil and Mexico, both of which have four points.