Who Conquered the Great Civilizations of Mesoamerica and South America?

The question contains a geographical error: there were no "great Indian nations in South America" in the sense implied. The major pre-Columbian civilizations were located in two distinct regions:

Mesoamerica (Mexico & Central America)

• Aztec (Mexica) Empire – Conquered by Spain (Hernán Cortés, 1519–1521)
• Maya Civilization (city-states) – Conquered by Spain (Francisco de Montejo, others; 1520s–1697)
• Other cultures: Zapotec, Mixtec, Totonac, etc. – Conquered by Spain

Andean South America

• Inca Empire (Tawantinsuyu) – Conquered by Spain (Francisco Pizarro, 1532–1572)
• Pre-Inca cultures (Moche, Chavín, Nazca, Tiwanaku, etc.) – Had already declined or were absorbed by the Inca before Spanish arrival.

The Conqueror: Spain

In both regions, the conquering European power was Spain. Spanish conquistadors, backed by the Crown, used military technology, indigenous alliances, and introduced diseases (smallpox, measles) to topple these empires in the 16th century.

Portugal colonized Brazil (Treaty of Tordesillas), encountering diverse tribal societies but no centralized empire comparable to the Aztec or Inca.

So: Spain conquered the great civilizations of Mesoamerica (Aztec, Maya) and the Andes (Inca). The term "Indian nations" is outdated; "Indigenous civilizations" or "empires" is preferred.