How were the Greeks able to defeat the persain

fleet even though they were outnumbered

Sparta held Xeres at Thermopylae, granting time for the Athenians to run the Marathon and build fortifications against a Persian invasion. Then the Greek "navy" came into play. From the beginning of Greece, the navy was vital in trade and in seafaring quests. The Greek dominance of the Sea was vital to the defense of their homeland and their honor.