The world champions, whose previous match was a 0-0 draw with Cameroon in March, started brightly with Vincenzo Iaquinta heading against the bar in the third minute, but the harrying Mexicans then took over with far neater play.
The lively Giovani Dos Santos found Carlos Vela unmarked in the Italian penalty area and the Mexican striker comfortably scored in the 16th minute.
"I don't think we could have met a worse team today," said Italy coach Marcello Lippi, explaining that his team had only just completed 10 days altitude conditioning and were not fully match fit.
"There are no alarm bells... We need to get fit gradually and peak at the right time. It's true I expected to see us better prepared physically," he told a news conference.
"I know these players very well, I'm not sad at all. It's important to be in the right condition in 10 days or so."
"The result is less important than what we have shown today. You can see in the changing room. They are serene, quiet and happy with the outcome," he said.
"I'm happy with the result, but I think we should be scoring more goals and letting fewer in," he added.
