First-half strikes from Paul Aguilar and Raul Jimenez put the host in control, with Oribe Peralta's double and Rafael Marquez's effort extending its 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 host, which enjoyed 75 per cent of the possession, will take a healthy advantage into next Wednesday's second leg in Wellington.
Coach Miguel Herrera's decision to select national-based players only, leaving the likes of Javier Hernandez and Carlos Vela out, meant there were seven changes for Mexico from the side beaten by Costa Rica in its final qualifier.
The visitor made three changes from its goalless draw with Trinidad and Tobago in October, with Leicester City striker Chris Wood chosen to lead the attack.
After a cautious start to the match from both sides it was Mexico that slowly began to exert some pressure, and eventually it carved out some good chances.
In the 18th minute the host thought it had scored when Jimenez hooked a shot towards goal, only for Glen Moss to punch clear on the line.
Moss continued to thwart Mexico's attacks with saves from Francisco Rodriguez and Jimenez, but he was at fault for the opening goal in the 32nd minute.
The goalkeeper failed to claim a cross from the right, and in the confusion Aguilar pounced on the loose ball to score his third international goal.
Mexico doubled its lead five minutes before the break when Jimenez found the back of the net with a close-range header.
Peralta capped a flowing counter-attack to increase the advantage in the 48th minute.
Miguel Layun raced clear down the left and rolled a low cross to Peralta and he slid in to tap home.
Richard Herbert made three changes in an attempt to stop the Mexican charge, and the visitor did begin to have more possession but lacked an attacking threat.
Peralta doubled his tally with a powerful header from a Layun cross with 10 minutes to play, and Marquez seemingly wrapped the tie up three minutes later with a simple headed finish.
The All Whites had some cause for cheer, though, as James netted an acrobatic volley from a Rory Fallon knock-down with five minutes left.