I understand that the Mayan classical era was long since over by the time the Aztecs moved into nearby southern Mexico. Nahuatl isn't related to Mayan languages, but the Aztecs practiced human sacrifice and played the ball game, like the Mayans and the Olmecs before them. Why? And what else did they pick up from the Mayans, and how? What is the connection between these people over in the East, whose urban society collapsed 800-1000, and these Nahuatl-speaking neighbours over to the West?
The connection is through what we might call a general Mesoamerican cultural tradition. To offer a comparison, the similarities between the Maya and Aztec are like those between the Greeks and the Romans, or even the Aryans. Zeus, Jupiter, Dyaus Pitar all represent analogus gods. The similarity is due to the fact that Greek, Roman, and Aryan cultures can all be traced to a proto-Indo-European culture. A similar Mesoamerican cultural tradition links the Aztecs, Maya, Olmec, Tarascans, Mixtecs, etc. Also, cultural traits can spread and be shared across languages, so even if the Maya and Aztec did not speak similar languages, they might still appropriate similar cultural practices.
You might check out Prehistoric Mesoamerica by Richar Adams.