Homer's Iliad depicts several duels between great warriors of the opposing sides: Paris and Menelaus, Hector and Ajax, Hector and Achilles. Modern fiction set in feudal Japan often depicts battles beginning with a duel to the death between two samurai between the armies. I'm sure it would be easy to find other (semi-)fictional sources depicting champions dueling each other at the site of a battle.
So, my question is... was this actually a common practice anywhere in the world? What did it resolve? Would the victor "win" the battle, and the loser withdraw? Or would the armies still do battle anyways?
I've talked about this wrt feudal Japan here. Also, a more common thing seen pre-Sengoku era was still duels between opposing soldiers, though not in the sense of 'champions' but rather pairing off two sides during the battle.