You have no idea how complicated a question this is, but yes. Yes, he could. Whether or not that won the battle varies.

My sources are this range from primary sources, such as The Anglo Saxon Chronicle, William Wheeler's memoirs, and the writings of Anna Komnene, ''The Alexiad''. Secondary sources include 'The Crusades: The War For the Holy Land' by Thomas Asbridge, Anglo-Saxon Military Institutions on the Eve of the Norman Conquest by Warren Hollister, and War for America: The Fight for Independence 1775-1783, by Jeremy Black. A more general book by Michael Howard, War in European History. Now that's out of the way, I'll answer the question.

In various forms of conflict, yes it could. At the Battle of Stamford Bridge in September of 1066, a famous Norse warrior held off the Saxon host as they attempted to stream across a bridge and attack the resting, unready Norwegian army of King Harald Hardraada. The Chronicle states that he held them off, killing over forty Saxon fyrd and only being felled by a spearman floating in a barrel beneath the bridge. Now, this delayed the Saxons, it demoralised them, and gave the Norwegians valuable time to put on armour, ready weapons and form battlelines. It certainly had an impact upon the battle.

Did it win the battle? No. The Saxons annihilated the Norse army after breaking through the shieldwall. But because of the great loss of Saxon fyrd and housecarls at Stamford Bridge, the Saxons fought the Normans lacking a great deal of their strength.

Another good example is the Battle of Evesham. Here, in 1265, a group of skilled knights were tasked with hunting down and killing the rebel leader, Simon de Montfort and his son. Though the battle was hideously one-sided, the decisive targeting of a political rival had a great impact upon the war itself - it ended it. It harks forward to the battlefield assassinations of the Plantagenets during the Wars of the Roses.

I suspect you're looking for something snappy. Something you can point to and say 'because this man did this, he won a battle'. These moments are rare...or, more accurately, they're very difficult to verify. Concepts like Horatius Cocles at the bridge and champions duelling are common in ancient and early medieval history, but it's very difficult to find one that you can pin down and use it as a good example.

Even the death of General Simon Fraser at Bemis Heights in 1777 we are unsure of; traditional legend is that it was a specific shot by Timothy Murphy, but generally it's considered an urban myth. However, whoever did kill him certainly helped win that battle.

See, that's why I said yes. Generals die a lot in warfare. Marmont is rendered hors de combat at Salamanca, as is his successor, Clausel. Gustavus Adolphus's death at Lutzen nearly broke the spirit of his army. However, Theodoric the Goth's death supposedly did very little to effect Visigothic strength at the Battle of Chalons.

It's a convoluted issue. Battles are some of the most monumental struggles we've ever created. Holding formation, you're right, is extremely important, as unit cohesion in Macedonian Phalanxes, Anglo-Saxon shieldwalls, German/Swiss Pike squares and even Mongol Tumans is all important. But occasionally, simply killing the right man or holding the right spot, soldiers had a very real effect on battles.