What was the name of the naval battle that decided Cleopatra's fate?

The naval battle that decided Cleopatra’s fate was the Battle of Actium. Fought on 2 September 31 BC near Actium on the western coast of Greece, it pitted the fleet of Octavian against the combined forces of Mark Antony and Cleopatra VII.

The battle was the climax of a political and military struggle that had grown out of the collapse of the Second Triumvirate. Cleopatra supported Antony with ships, money, and supplies, while Octavian presented the conflict as a defense of Rome against a foreign queen and her Roman ally. Octavian’s admiral, Marcus Vipsanius Agrippa, helped isolate Antony’s forces before the fleets met.

Cleopatra’s squadron broke through the Roman line, and Antony followed her, leaving much of his fleet behind. Their defeat destroyed their political position. They retreated to Egypt, where Octavian invaded the following year. Antony and Cleopatra died in 30 BC, and Egypt became a Roman province. The battle also helped mark Rome’s transition from republic to empire. It is sometimes confused with the later fighting at Alexandria, but Actium was the decisive naval engagement.