Chris James and Rory Fallon added two late consolations but Carlos Alberto Pena settled matters for Miguel Herrera's side, who can now begin preparations for the World Cup
Miguel Herrera's men were all but guaranteed to progress prior to the second leg in Wellington, having romped to a 5-1 victory on home soil last week.
Any hope of a miraculous New Zealand fightback was swiftly snuffed out by Peralta, who scored in the 14th, 29th and 33rd minutes to essentially confirm Mexico's progression.
The hosts, who saw Jeremy Brockie have a penalty saved in the 39th minute, at least had the consolation of grabbing two late goals in reply - through Chris James and Rory Fallon - but Mexico had the final say through Carlos Alberto Pena's 86th-minute strike.
Mexico, who countered with pace and precision throughout, will now play at the World Cup finals for the 15th time, but outgoing New Zealand coach Ricki Herbert can take heart from the spirit his side showed in the second half against a side 55 places above them in the world rankings.
In his final match as New Zealand coach, Herbert threw youngsters Storm Roux and Bill Tuiloma into the spotlight in front of over 37,000 fans at Westpac Stadium.
The duo displayed promise and Mexico were forced on to the back foot in the opening stages before Peralta found the net with a chipped finish to virtually condemn the game to exhibition status.
Miguel Arturo Layun and Pena each laid on further goals for Peralta as the visitors threatened to run riot.
Yet New Zealand did their best to send Herbert out in style, powering forward after the break and eventually gaining reward when James - a scorer in the first leg - made no mistake with his side's second penalty of the game in the 80th minute.
An unmarked Fallon converted a cross from Brockie three minutes later to further reduce New Zealand's arrears, before Pena rounded off a fine individual display with Mexico's fourth.