Giovani Dos Santos had a volley and a header disallowed, with replays suggesting both calls were incorrect.
Cameroon rarely threatened but a Samuel Eto’o shot hit the post and Benoit Assou-Ekotto’s free-kick went wide.
However, Mexico secured victory when Dos Santos’s shot was parried before Peralta arrived to slot in the rebound.
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.
There were questions about how these countries would fare, with both sides changing managers in scraping through World Cup qualifying.
A nimble Mexico, though, appeared determined to make the most of their time in Brazil, while a powerful-looking Cameroon showed their struggles had continued into the tournament.
The African side struggled to deal with the wing-backs in the 5-3-2 formation employed by the Aztecs, who appeared to have a legitimate early goal disallowed.
Giovani Dos Santos was on loan at Ipswich from Tottenham five years ago.
Hector Herrera crossed from the right and forward Dos Santos scored a left-foot volley only for the effort to be ruled out for offside, even though replays showed the strike should have stood.
Cameroon almost made it worse when left-back Assou-Ekotto followed up a marauding run by picking out Eto’o, whose first-time shot hit the outside of the post.
Mexico might have felt annoyed they were not in front and their grievances were added to when they had another goal controversially disallowed and a penalty shout rejected.
First, Dos Santos’s header from a corner was ruled out, then the striker had a penalty shout turned down following a challenge from Aurelien Chedjou.
However, Mexico had only themselves to blame for not taking the lead just after the break. Dos Santos helped on a pass to release Peralta only for the striker to have his shot saved by onrushing keeper Charles Itandje.
The miss was almost punished when Assou-Ekotto’s free-kick deflected just wide before Mexico’s frustration turned to joy.
A Dos Santos shot was initially parried by Charles Itandje but Peralta was on hand to drive in the loose ball home for the winner.