Two RBIs from right-fielder Donny Hale set the tone for the offence while veteran Jarrad Martin - playing in his fifth world champs - hit a solo home run.
New Zealand came into the tournament in patchy form, having lost to local club sides but won warm-up games against South Africa and the Czech Republic. They carried the latter results into the top of the first inning against Mexico, with Hale's one-out single enough to drive in Tyson Byrne after the shortstop reached with a triple.
The Black Sox threatened to blow things open in the second but settled for three runs after Brad Rona flied out with the bases loaded. Mexico pitcher Gabriel Melendez struggled with his command throughout the inning, giving up a lead-off home run to Martin before hitting two batters and walking Hale with the bags full.
Mexico made a pitching change in the fourth but Oscar Martinez wasn't much more effective. After walking Tyron Bartorillo, second baseman Nathan Nukunuku - a late call-up to the squad to cover for injured captain Rhys Casley - smoked a grounder up the first base line to score Bartorillo and make it 5-0.
The offence was kept quiet from there, but Hayes held the lead and the Black Sox took the win.
New Zealand face another minnow in Colombia tomorrow afternoon, before tougher tests in the form of Japan, Canada and Argentina await next week.