Niko Kovac's side had impressed in spells against Brazil in their opening match and their class told in this encounter, with the outcome rarely in danger from the 11th minute onwards. That was when Ivica Olic, 34, became his country's oldest World Cup goalscorer, firing home first time with his left foot after being teed up at close range by Ivan Perisic's perfectly weighted pass.
This goal was something of a personal disaster for Charles Itandje, whose botched clearance was seized upon at the halfway line by Perisic. Plenty of work remained to be done, but the Wolfsburg midfielder's pace took him clear in the left channel and he deceived Itandje by shaping to cross and instead side-footed into the net at the keeper's abandoned near post.
Croatia continued to dominate and Mandzukic could and should have added a third shortly after when he raced clean through only to delay his shot too long and, under pressure, scoop the ball wide. But the Bayern Munich striker would not be denied, and he completed a brace midway through the half. The first saw him rise unchallenged at corner to bullet home a downward header, while the second came about when he profited from another mistake by Itandje, who spilled a tame Eduardo shot at the feet of Croatia's predatory No17.
The scoreline offered just reward for Kovac's side's overall superiority, and they will now hope to continue their free-scoring ways against a Mexico team that shut out the hosts.