The Persians lost the battle. The Athenian army defeated the Persian expeditionary force.
Marathon was a plain, not a city. It was owned by Athens. They fought a battle against a Persian amphibious punitive expedition sent by Persia in 490 BCE.
They hung about in the hills around the Plain of Marathon, where the Persian cavalry could not get at them, for reinforcements from Sparta, and then saw the Persian cavalry being embarked on ships. so they ran down and defeated the inferior Persian infantry.
The Greeks allowed the center to give way thus exposing the Persian flanks to a concerted Greek assault causing the collapse of Persian forces who then sought to escape by sea - the Greeks then slaughtered the Persian forces attempting to escape . Look to the related link below which has an excellent representation of what occurred at the seminal battle of Marathon .
Their armoured infantry were superior to the Persian infantry but were wary of the Persian cavalry on open ground on the plain of Marathon. The Athenians with their ally Plataia lurked in the hills waiting for the Spartans to arrive, but when they saw the Persian cavalry being embarked on the Persian fleet, they took the opportunity to run down and defeat the unprotected Persian infantry.
It was not the Greeks, it was Athens and its ally Plataia. The Athenians waited on the edge of the Plain of Marathon for reinforcement from Sparta. Then saw the superior Persian cavalry being embarked on ships and ran down and defeated the unsupported inferior Persian infantry.
The Battle of Marathon was won by Athens and its ally Plataia in 490 BCE.
The Greeks , specifically the city-state (polis) of Athens , were capable of defeating a numerically superior Persian army was through superior armor and tactics ~ see related link below ,
The Battle of Marathon .
Athens won at Marathon. Rome won against Carthage.
Peace.
Marathon , Greece
Marathon, Greece .