Oribe Peralta scored in the 61st minute to secure the victory against their african opponents.
At a rain-lashed Estadio das Dunas in north-eastern city Natal, Cameroon almost stole a point late on when Benjamin Moukandjo's free header was acrobatically saved by keeper Guillermo Ochoa.
An equaliser would have been harsh on a Mexico side who put on an impressive performance, combining a strong work ethic with an attacking threat, and should serve them well when they play hosts Brazil on Tuesday, 17 June.
Peralta's seventh goal in nine competitive games prevented the dubious refereeing decisions from overshadowing the victory, while Cameroon's quality and prospects of getting into the second round appear limited with Croatia and Brazil to come.
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