The aura of it has dissipated slightly in recent times - Mexico emerged with only one win and three goals in five matches there during the Hexagonal - and the All Whites have to believe a result or narrow defeat is possible in the first leg. The two teams meet again in Wellington on November 20.
"It was pretty intense," said All Whites coach Ricki Herbert, who witnessed Mexico's final home game against Panama last weekend. "It's a very passionate part of the world. In any sporting code, you want to test yourself against the best in the best environments. And Mexico at the Azteca is certainly that.
"When I played at the World Cup [in 1982] we played arguably the best Brazilian team of all time. If you're not prepared to put yourself up against the best, that's disappointing and I know this group will be raring to go."
The All Whites will prepare in Los Angeles, gathering there no later than November 9 and flying late into Mexico City. It's a similar approach to the one they used in 2009, when they based themselves in Dubai before heading to Manama on the eve of the 0-0 draw with Bahrain.
The details of the first Mexico game are yet to be confirmed but it's been reported it will be at 2pm on November 13 (local time) when the heat and smog will be at its worst.
The All Whites have played El Tri twice in the past four years, going down 2-0 in Pasadena in 2010 and 3-0 in Denver in 2011. New Zealand won the only other match between the sides when current All Whites manager Brian Turner scored a double in a 4-0 win in 1980.
The Mexicans will expect to win but they will come under enormous pressure. They are hugely grateful to the US for keeping their chances alive but it has been uncomfortable and veteran Rafael Marquez summed up fans' feelings.
"The situation is lamentable," he was quoted as saying on goal.com. "I hang my head in shame and it's embarrassing for us to qualify [for the playoff] like that."
Failure against the All Whites is not an option.