The Battle of Salamis ~ see related link below .
Battle of Marathon 17th September 490 bc
Which battle.
Take your pick - Salamis, Mycale, Eurymedon, Cyprus and others.
Salamis.
Which battle - there were many, but the Greeks won by superior strategies and tactics.
Battle of Salamis and later at the Battle of Plataea
They defeated them in a sea battle at Salamis.
Late August 480 BC
Salamis, Plataia, Mykale, Eurymedon, Cyprus.
It was not the Greeks but the Greek city-state of Eretria.The Persians then switched to Athens which defeated them at Marathon.
There were many battles. The Greeks used better strategies and tactics. They were also operating on internal lines, the Persians on external lines.