Croatia bounced back from their opening defeat to hosts Brazil to keep alive their hopes of progressing from Group A with an emphatic display. (Agencies)
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.
The Indomitable Lions seemed anything but as they imploded with full-back Benoit Assou-Ekotto even trying to headbutt team-mate Benjamin Moukandjo in the dying moments following an argument.
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.
Olic met a Perisic pass at the far post and buried his shot past Cameroon goalkeeper Charles Itandje, then nearly added a second five minutes later.
Things went downhill for Cameroon as Barcelona's Song became the third player to be sent off at the World Cup, after Portugal's Pepe and Uruguay's Maxi Pereira.
Referee Pedro Proenca spotted Song lashing out at Mandzukic on a Croatian counterattack and he produced a red card on 40 minutes.
Perisic grabbed Croatia's second on 48 minutes when he unleashed a powerful shot after a strong run.
Mandzukic, who has said he wants to leave Bayern Munich with Poland striker Robert Lewandowski set to arrive from Borussia Dortmund, then grabbed his brace.
He headed home from a corner on 61 minutes before firing in his second on 73 minutes when he tucked home the rebound after Itandje saved a shot from substitute Eduardo.
Barcelona's new signing Ivan Rakitic squandered a golden chance to claim Croatia's fifth just before the final whistle while Moukandjo hit the bar with a late header, before tangling with Assou-Ekotto.
Finke's Cameroon will now be playing just for pride when they face Brazil in Brasilia on Monday.
Croatia bounced back from their opening defeat to hosts Brazil to keep alive their hopes of progressing from Group A with an emphatic display.