In which sense? Athens never triumphed over Sparta, they just survived, and you know why? Wikipedia tells you:
Corinth and Thebes demanded that Athens should be destroyed and all its citizens should be enslaved. However, the Spartans announced their refusal to destroy a city that had done a good service at a time of greatest danger to Greece
In which sense? Athens never triumphed over Sparta, they just survived, and you know why? Wikipedia tells you:
Doesn’t quite match your narrative, does it?