If you mean that you achieved a tie score, you can say i finally evened the score." "I evened the game" doesn't sound natural.

No it is not very clear what you mean (especially without a context).Can you give a specific example of what you want to say?

This would make sense if a situation (figuratively) or game (literally) was unequal by some means but after a change, became level for both parties. Hope this helps!

Honestly it is not a great sentence. I think you are trying to say "I finally drew level." If not let me know and I will try again.

"I finally tied the game" is what you would want to say. "even" means that something is the same, or equal, however you wouldn't want to use the word "evened" (the past tense of even) in this context.