Final answer:
Francisco Pizarro defeated the Inca Empire by capturing their leader, Atahualpa, and establishing Spanish control over Peru.
Step-by-step explanation:
The Spanish conqueror who defeated the Inca Empire was Francisco Pizarro. In 1532, Pizarro captured the Inca leader, Atahualpa, and executed him the following year. Pizarro then seized control of Cuzco, the Inca capital, and established Spanish control over Peru.