Morgan Plata scored a goal in each half, his second in the 34th minute to pull Mexico within 3-2, but Rodolfo Fortino tallied his second of the match less than a minute later and Luca Leggiero tacked on additional insurance in the 36th to send Italy to the second round with a third consecutive victory.
Italy outshot Mexico 61-15, 22-9 with chances on goal.
"We played well at the start of the match, with a good strategy," Mexico coach Ramon Raya said. Sometimes we lack experience but that's normal for a team like us. Unfortunately this is a sport that doesn't forgive any mistakes and we took too many risks when the score was 3-2."
Mexico becomes the second team from CONCACAF to be eliminated, joining confederation champion Costa Rica.