After scoring just three goals in their last four CONCACAF qualifiers at home, Mexico rediscovered their scoring touch as they outclassed the Oceania champions at the Azteca Stadium.
"The team were sensational, I'm very happy because the lads did a phenomenal job, they gave their all," said Mexico coach Miguel Herrera.
"We needed an aggressive and dynamic team with lots of determination because we needed to win the match."
Striker Oribe Peralta scored twice in the second half and Rafael Marquez added the fifth.
"The worst we can do is think it's settled," Peralta said.
"We must win there and we still have a lot to improve. We're a small step from getting what were looking for."
Mexico have qualified for every World Cup since they hosted the finals in 1986, with the exception of 1990 when they were banned by FIFA after fielding over-age players in a youth tournament, but almost failed this time.
The CONCACAF region's traditional heavyweights were minutes away from missing out on the play-offs altogether when they were beaten by Costa Rica last month but survived only after Panama blew a 2-1 lead against the US, who qualified automatically along with Costa Rica and Honduras.
"We're not at all overconfident, we're not thinking this is over, it's a 0-0 draw for us and we're going to start from zero," Herrera said.
"It was important not to get desperate until we got the first goal. The team didn't lose their concentration.
"I can see myself coming back on the 21st (of November) with the (World Cup) ticket."
Under the guidance of Herrera, their fourth coach of the qualifying campaign, Mexico had no problems overcoming New Zealand, who allowed the Mexicans to dictate the match after adopting a defensive approach.
The All Whites have only qualified for the World Cup twice before and the odds were heavily stacked against them with their captain Winston Reid ruled out of the play-offs because of an ankle injury.
"It was always going to be tough for us and we made it tough for ourselves in certain areas," New Zealand coach Ricki Herbert said.
"We pride ourselves in certainly defending better than we did tonight and that was always going to be costly against a very good side."
Mexico dominated possession from the outset on Wednesday but needed more than half an hour to get the ball past New Zealand keeper Glen Moss, who pulled off a string of spectacular saves during the match.
But a mix-up with defender Andrew Durante in the box left Aguilar with an open net for the first goal, before an unmarked Jimenez headed in for the second goal off a corner.
Oribe scored three minutes into the second half when he tapped in a low cross from Miguel Layun, then added his second when he again combined with Layun.
New Zealand were facing the prospect of a rout in the energy-sapping high-altitude Mexican capital when Marquez made it 5-0 with six minutes still to go.
But James caught the home team napping when he scored a minute later with a shot that hit the post and dribbled over the line.
"The defending off crosses, allowing players free in the box at crucial times, we've always been incredibly strong in that area," Herbert said.
"That's more disappointing for me ... the way we conceded the goals."
- Sports & Recreation
- New Zealand
- Oribe Peralta
- Paul Aguilar