[KyleGoetz]

TO go with KurumuHatake's attempt (and arriving at what masaegu said):
私の = my
最後 = final
の = links "final" with:
勝利 = victory

Random thought: I believe, when deciding whether to use 最後 or 最終, the former is used for discrete lists, while the latter is used for continuous things. To put it another way, the first identifies a "last individual," while the latter is more like a "the end is upon us"-type feeling.

To make a couple examples (I hope I make correct examples!):
If you're at a chocolate factory that is closing down: これは最終のチョコだ。 (it was continuously churning out chocolate, and this is the final chocolate coming across the conveyor belt)
If you're eating out of a box of chocolates: これは最後のチョコだ。

Also, you might talk about, in a TV series coming to a close, 明日はとなりのサインフェルドの最終だ。

On the other hand, I believe both of these sentences are correct (although they carry different nuances, which I'm not privy to):
最後のランナーがゴールした。
最終のランナーがゴールした。
They both talk about the last runner finishing the race, but I think the first is identifying the last runner specifically, while the latter is more like implying there has been a continuous stream of runners finishing, and this is the end of the stream.

I hope I was correct and also made sense.