Peruvian Indians drag the Spanish governor, Alvaro, into the square and are about to execute him. Suddenly Zamoro, an Inca, appears and asks them to release the man; they do so.
Zamoro tells the Indians that he had been captured and tortured by Gusmano, the leader of the Spaniards (Un Inca, eccesso orribile / "An Inca..dreadful outrage!") to the point where everyone believed him to be dead. Otumbo tells Zamoro that Alzira, his beloved, along with her father Ataliba, are being held captive by the Spaniards, and he urges the Indian tribes to revolt: Risorto fra le tenebre / "I emerged into the darkness...").
Scene 1: The main square of Lima
Alvaro announces that, due to his age and infirmity, he is relinquishing the governorship and handing it over to his son, Gusmano who states that his first act will be to secure peace with the Incas. Ataliba gives him his support, but advises him that his daughter Alzira is not yet ready to marry Gusmano. He, while understanding (Eterna la memoria / "The eternal memory of a desperate love is weighing her down..."), urges the older man to try to persuade her (Quanto un mortal può chiedere / "Whatever a mortal man can ask for..")
Scene 2: Ataliba's apartments in the governor's palace
As her father enters, Alzira wakes but is still half dreaming of Zamoro. She recounts a more disturbing dream she has had of Gusmano (Da Gusman sul fragil barca / "I was fleeing from Gusman in a frail boat") but, although he is dead, she still believes that Zamoro loves her: Nell'astro che più fulgido / "On the star that gleams most brightly...there lives Zamoro". Ataliba continues to try to persuade Alzira to marry Gusmano, without success, until suddenly Zamoro enters. Believing that it is his ghost, Alzira is skeptical, but realizes that he is still alive. They pledge their love together: Risorge ne'tuoi lumi l'astro de'giorni miei! / "The star of my existence has risen again in your eyes!".
Gusmano enters, sees the couple together, and orders that Zamoro be arrested and immediately executed. As the Inca invasion of Lima is announced, Alvaro confirms that Zamoro has saved him from certain death; Gusmano orders him to be freed to go out to fight with the invading Incas: "I shall meet you in battle, hated rival".
Scene 1: The fortifications of Lima
Zamoro has led a fresh attack against the conquistadores and has been captured. Gusmano condemns him to death, but, over Alzira's protests, forces her to agree to marry Gusmano promising that he will spare Zamoro. Reluctantly, she agrees (Gusmano: Colma di gioia ho l'anima! / "My heart is bursting with joy").
Scene 2: A cave, some distance from Lima
The defeated Incas are downcast, but they hear that Zamoro has escaped, dressed as a Spanish soldier. He soon enters but is in despair: Irne lungi ancor dovrei / " Must I drag out my days as a fugitive, bowed down with shame?". When he hears from his followers that Alzira has agreed to marry Gusmano and that preparations are being made, vows to fight: Non di codarde lagrime / "This is not the time for cowardly tears, but for blood!". He rushes out to the palace
Scene 3: Large hall in the governor's palace
As the wedding of Alzira and Gusmano is about to begin, a Spanish soldier leaps forward and fatally stabs Gusmano. To Alzira's surprise it is Zamoro. Before he dies, Gusmano tells him that Alzira only agreed to the marriage in order to secure his release. He forgives Zamoro, blesses his union with Alzira, and receives a final blessing from his father as he dies.