Ivica Olic gave Niko Kovc’s men the lead after just ten minutes before Alex Song saw red after appearing to lash out at Mario Madzukic in an off the ball incident.
With ten men, Cameroon’s task became more difficult as they went further behind to an impressive solo goal from Croatia wideman Ivan Perisic.
Frontman Mandzukic made sure of the victory with a brace late on.
The Indomitable Lions follow Australia and Spain through the exit door.
Cameroon: Itandje, Mbia, Chedjou, N’Koulou, Assou-Ekotto, Song, Matip, Enoh, Choupo-Moting, Aboubakar, Moukandjo.
Sent off: Song.
Croatia: Pletikosa, Srna, Corluka, Lovren, Pranjic, Modric, Rakitic, Perisic, Sammir, Olic, Mandzukic.
Scorers: Olic, 10, Perisic, 47, Mandzukic, 59, 72.
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