Goals from Paul Aguilar, Raul Jimenez, Oribe Peralta and Rafa Marquez have put Miguel Herrera's men firmly in control of this tie
First-half strikes from Paul Aguilar and Raul Jimenez put the hosts in control, with Oribe Peralta's double and Rafael Marquez's effort extending their advantage after the interval.
New Zealand battled hard to stay in the game and added a late consolation through Chris James at the Estadio Azteca.
But the hosts, who enjoyed 75 per cent of the possession, will take a healthy advantage into next Wednesday's second leg in Wellington.
El Tri entered the play-off looking to end a disastrous 2013 on a high note to reach the World Cup. In order to do so, the federation went through three coaches over the last six weeks before deciding on Club America manager Miguel Herrera to guide the national team to Brazil next summer.
Herrera did not join the team quietly. After leading Mexico to a win over Finland in a friendly last month, the coach made headlines when he decided to choose an all domestic-based squad for the two-leg playoff against the All Whites, leaving big names Javier 'Chicharito' Hernandez, Giovani dos Santos and Hector Moreno in Europe for the games.
Herrera, who has not ruled out bringing back the European-based players should Mexico hold on and qualify for the World Cup, added seven Club America players to the squad. And the decision paid off early on against 79th-ranked New Zealand.
Two of Mexico's four scorers (Aguilar and Jimenez) play for Club America, who play their matches at Estadio Azteca and are the reigning Liga MX champions.
It was said before the match that New Zealand would need to rely on a solid defence to hold off Herrera's attacking style of play, but the All Whites' back line had no answer from the start. Goalkeeper Glen Moss did all he could but Mexico's 21 shots were too much to handle.
The hosts were first to threaten when Jimenez nearly scored from a cross before Moss slid across to make the save. Moments later, Moss got his fingertips on a long Maza Rodriguez shot to deflect the ball off the crossbar.
It took El Tri 10 shots before they finally found the first goal thanks to Aguilar being at the right place at the right time to pick up the rebound off a headed clearance by Andrew Durante.
El Tri kept the pressure on and nearly found their second after Peralta beat the defence to tap in an Aguilar pass, but the forward was called offside. Moss then had to make a couple more spectacular saves before Mexico would find their second to build a nice cushion heading into half-time.
New Zealand's defenders struggled in all aspects of the game, but their poor marking off a Mexico corner left Jimenez wide open inches from the goal. And if they thought they had made any adjustments to stop the attack at half-time, they were wrong.
Peralta got his seventh goal in as many international games when he made it 3-0, scoring from a Miguel Layun cross after good work from Rafa Marquez.
By this point, New Zealand still hadn't had a real opportunity as Mexico dominated possession, but the hosts weren't done.
With 20 minutes left to play, Peralta headed in Mexico's fourth unanswered goal. Just minutes later, Marquez decided to get into the scoring action with a header of his own to leave New Zealand with a huge mountain to climb to reach their second successive World Cup.
The one bright spot for the All Whites came in the 84th minute as James scored, but there was no celebrating from the visitors. After watching Mexico hold the ball for 73% of the time, it may take a miracle for New Zealand to eliminate the dominating El Tri side, which is one game away from its seventh consecutive World Cup.