Croatia bounced back from their opening defeat to hosts Brazil to keep alive their hopes of progressing from Group A with an emphatic display.
But Cameroon were largely the architects of their own downfall after playing the last 50 minutes with 10 men after Alexandre Song's dismissal for a stupid reckless punch to Mandzukic's back.
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Croatia, for their part, could have doubled their score but at least did what they needed to.
Veteran striker Ivica Olic gave them a 1-0 half-time lead before his Wolfsburg team-mate Ivan Perisic added a second ahead of Mandzukic's brace.
The result leaves Niko Kovac's Croatia third in the table, just one point behind joint leaders Brazil and Mexico. Cameroon are bottom with no points.
Croatia now face Mexico in Recife on Monday for a place in the last 16.
Cameroon were hamstrung before kick-off when captain Samuel Eto'o lost his battle to make the starting line-up having failed to recover from a knee injury.
Mandzukic returned for Croatia in style having missed their opening defeat to hosts Brazil through suspension, breathing life into their last 16 hopes.
They needed just eleven minutes to take the lead as Cameroon failed to bounce back in tropical Manaus after their opening 1-0 defeat to Mexico.
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