When the Shadows said "they will not follow you if you are dead" and tried to destroy the White Star and the cruiser did the only thing it could do to defend them and moved between them.... That was when it was won. Vorlons and Shadows could make people die. They could not make people die for them. Even if they wiped out every single one of the younger races they could not win because the younger races would no longer submit. That is triumph over adversity beyond winning by force of arms.
The First One simply helped them realize it was over. When no matter what you do you will never get what you want there is nothing left to be won. And while the Vorlons and Shadows were petty enough to have wiped everyone out from pure spite they were not going to do it with the First One watching.
In real life, there is no First One to help the antagonists come to higher realization. There is only one prevailing over the other. The epistemology of the whole thing was dissatisfying to me.
Chalk it up to a personality flaw on my part...