In the case of the Aztecs, they quite arguably happened to run into someone even more destructive, punitive, insular, judging, self-righteous, and violent then they were.
Cortez and his 300-odd men could never have taken down the Aztecs, were it not for how all their neighbors hated them so passionately that they'd rather be ruled by smelly, strange-looking, gold-hungry space aliens.
The diseases certainly had an effect (after the Night of Sorrow and before the conquest of Tenochtitlan, smallpox struck the whole Valley of Mexico); but Tlaxcala had an effect too, and if the Aztecs' subject peoples had rallied to their arms in the same way the Tlaxcalans rallied to the Spanish (after some initial fighting against them), there's no way Cortez could have won.
The Aztec Empire wasn't even 150 years old; if memory serves, Tlacallel flourished about 80 years before Cortes. Nor were they in decline -- Montezuma had stopped the empire's opportunistic conquests, and was focused on conquering the independent countries that still formed pockets of resistance geographically surrounded by the Aztecs. Tlaxcala was the most important of these, as it happens...
The empire is not the civilization. The civilization arguably goes back more than 1000 years, certainly since the Toltecs, which was a considered successor and collector of the Olmec, Teotihuacano and Maya people's cultures. The Aztecs themselves considered the vanquished Toltec their cultural superiors. By the time Montezuma II came to power, the Aztec world was already winding down, consumed by resource wars; and had entered a period of insular medieval-like culture that shunned their once great, open cities in favor of fortress-like enclaves.