The Athenian navy did not defeat the Persian navy. There were several naval battles between combined Greek city fleets which defeated Persian fleets from 480 to 449 BCE. They defeated the Persian fleets by a combination of good strategy and tactics.
The Greeks recognised that their only hope against the more numerous and heavier Persian ships was to get them in narrow waters where they could be outmanoeuvred by the more agile Greek ships, whose principal weapon was the ship's ram. They tried this first in the strait at Artemesion where the stand at the Thermopylai pass forced the Persians to try to turn the position by sea, but the battle was lost.
They retired to the strait between Salamis island and Athens to try again. This was a better location, as the Persian fleet had to split in two narrow columns to get through the channel on each side of the island of Psyttalia, and exposed their flanks to the waiting Greek ships ramming tactics.
The balance of forces was also much helped by further debilitating the Persian fleet - Greek agents persuaded the Persians that the Greek fleet would not stand for battle, but escape through the back passage past Megara. The Persians sent the Egyptian third of their fleet around to cover this, and so the numbers of ships on both sides were evened.
They also persuaded the Persians that the Greeks might surrender, so their ships sat at oars all night outside the bay in a swell waiting and were exhausted by the time they closed in for battle the following day.
King Xerxes sat on a headland to watch the battle. He had need to give his supervision as his remaining ships were from Phoenicia and the Greek cities within his empire, and so were not all that enthusiastic about fighting for Persia anyway.
So what appeared to be a dominant Persian fleet was in fact reduced in numbers, fitness for battle and enthusiasm for the cause, and caught in a disadvantaged tactical deployment in the narrow waters.
It lost the battles of Lade 493 BCE and Artemesion 480 BCE then won the battle of Salamis 480 BCE,Eurymedon 466 BCE and Cyprus 450 BCE.
They defeated the Persians in combined land and sea battles at Cyprus in 450 BCE, after which the Persians agreed to peace, ending a 50-year war.
There were several naval battles. Which battle did you have in mind?
The Persian leader defeated by the Greeks was Darius.
Xerxes.
The small Greek force at Thermopylae was defeated by the Persian army in 480 BCE.
At Marathon and Salamis, the Greek cities defeated the Persian forces. At Thermopylai the Persian forces defeated the Greek cities.
Persian naval forces were defeated by a Greek naval coalition under the command of the Spartan Admiral Eurybiades.
The Persian leader defeated by the Greeks was Darius.
Its called ''the Persian wars'' or the ''Greco-Persian wars''.
479 BCE at Plataia.
Xerxes.
The small Greek force at Thermopylae was defeated by the Persian army in 480 BCE.
At Marathon and Salamis, the Greek cities defeated the Persian forces. At Thermopylai the Persian forces defeated the Greek cities.
Persian naval forces were defeated by a Greek naval coalition under the command of the Spartan Admiral Eurybiades.
It was the Battle of Thermopylae in the Second Persian War. The Greeks won. Shortly after Thermopylae the Athenian Navy defeated the Persian Navy at Salamis, and in the next year the Persian Army was defeated by a combined Greek Army at Plataea.
The Battle of Marathon .
The Persian navy comprising Phoenician, Asian-Greek and Egyptian fleets.
Cyprus 450 BCE.
They didn't defeat a war. They defeated the Persians in the Persian War in the eastern Mediterranean on land and sea 499-449 BCE.