The Bayern Munich man helped himself to two goals, following strikes from Ivica Olic and Ivan Perisic
Olic made the breakthrough 10 minutes into the first half, before team-mate Perisic sealed all three points following a brilliant solo run shortly after the break.
Mandzukic added some gloss to the score line in the 60th and 73rd minutes as Croatia won their first World Cup match since 2002, having lost three and drawn two.
Niko Kovac's men have now collected three points from two games and are one point adrift of Mexico, who are level on points with host nation Brazil heading into their final group game, while Cameroon remain winless and out of contention.
Attempting to respond to their defeat to Mexico, Cameroon coach Volker Finke was forced into a change up front, with captain Samuel Eto'o ruled out with a knee injury. Defender Cedric Djeugoue also made way for Joel Matip.
Croatia made three changes to the team that lost to Brazil last week. Mandzukic returned from suspension and he was joined in the line up by Danijel Pranjic and Sammir as Nikica Jelavic, Sime Vrsaljko and Mateo Kovacic dropped out.
The African side settled the quickest out of the two teams, though Croatia eventually found their groove to open the scoring in the 11th minute.
Perisic slipped the ball across the six-yard box for Wolfsburg team-mate Olic to fire home from close range - his 19th international goal since making his debut in 2002.
Cameroon's task was made a lot tougher just five minutes before the half-time interval, when midfielder Alex Song saw red for an off-the-ball incident.
The Barcelona player lashed out at Mandzukic, striking the forward on the back as Croatia pressed ahead on the counter attack.
It went from bad to worse for the Indomitable Lions three minutes after the break as Croatia doubled their advantage through Perisic.
The midfielder went from provider to goalscorer, driving into the area before placing the ball beyond goalkeeper Charles Itandje.
Cameroon's numerical disadvantage was evident and they almost went three goals behind following a swift counter-attacking move, however Mandzukic saw his effort go wide of the post.
The Bayern star finally got his goal on the hour-mark, rising highest to nod home Croatia's third from a corner and his 14th on the international stage.
The striker put the African nation to the sword again in the 73rd minute, tapping home an easy rebound after goalkeeper Charles Itandje's attempted save fell straight to the feet of the 28-year-old.