The Greeks and Persians fought in many battles between 499 BCE and 449 BCE. However two great Greek victories stand out. The first, a sea battle in 480 BCE was fought at Salamis. The second was a land battle at Plataea the following year. These two battles defeated the Persian invasion of mainland Greece.
The strong army that Alexander defeated was the Persian Army
hi
when he defeat the king darius 3
There were several. The most decisive was Gaugamela.
The attack was no surprise - the two armies were confronting each other. Alexander wanted to defeat the Persian army to gain control of the Persian empire.
Gaugamela.
Granicus, then Isus, then Gaugamela.
The battle of Marathon 490 BCE.
Granicus
Alexander the Great decisively defeated the Persians led by Darius the Third at Gaugamela (located in Iraq) October 1, 331 BC .
Alexander the Great defeated Darius, king of Persia in 331 BCE. This was at the battle Gaugamela, he did march through Bactria in 329 BCE, but he had already defeated the Persians.
I'm almost positive that he defeated the Persians at the Battle of Gaugamela.