On 14 October, 1066, the last Anglo-Saxon king of England died in battle.
(If you don't get the joke, it's because you haven't played Skyrim.)
Many people don't know that the Anglo-Saxon army that the Normans defeated had very recently fought and beaten a Viking army led by "the Thunderbolt of the North," King Harald Hadrada of Norway. Harald was a king with a storied career, having fought in the Vaering guards for the Byzantine emperors before returning to Norway to claim his throne. There's a whole book about him contained within the Heimskringla, the story of the Norse kings. He died fighting Harold Godwinson at the Battle of Stamford Bridge in the north of England. That battle was on 25 September. Barely had they defeated the Viking army when word came of the Norman invasion in the south. The Anglo-Saxons had to force-march their way across the country in order to catch William's Normans.
Nevertheless it is not thought to be exhaustion but communication that lost the battle for the Anglo-Saxons. They fought dismounted in a shield wall, as also did the Vikings. The Norman cavalry could not pierce the wall, but it could withdraw, plan, and re-engage. Once committed to the fight, Harold's forces had difficulty seeing the battle as a whole and reorganizing accordingly. The Normans could change plans as the battle progressed. In a demonstration of the concept that Colonel Boyd would later formalize as the "OODA loop," this increased capacity to communicate and respond to changes on the field is thought to have been the decisive factor at Hastings.
Few battles have changed history as completely as the Battle of Hastings. The Normans' rise to the leadership of England lasted for hundreds of years, and committed England as a nation to defending Norman possessions in France during the Hundred Years War. The expansionist Normans went on to conquer Wales, Ireland, and Scotland, only one of them with finality but setting the stage for the rise of Great Britain. It's hard to imagine what the world would look like today if the English had remained an Anglo-Saxon power content with England alone.