Final answer:
The Visigoths defeated the Romans in 378 CE at the Battle of Adrianople, killing Emperor Valens and marking a turning point in the decline of the Roman Empire.
Step-by-step explanation:
The decisive defeat of the Romans by the Visigoths occurred in 378 CE at the Battle of Adrianople. This monumental battle is a significant event in history as it marks the beginning of the end for the Western Roman Empire. The Visigoths, led by Fritigern, were able to decisively defeat the Roman army, killing the Emperor Valens in the process.
The aftermath of the battle signaled a shift in power as numerous Germanic tribes, including the Visigoths, subsequently invaded Roman territories and established their own kingdoms.