As a native speaker here in the US I agree that they can be synonyms, but they also have different nuances at times. I found a website that explains it more clearly than I'm able to, and I agree with their explanation of the difference between the two words: http://english.stackexchange.com/questions/67063/eventually-vs-finally
Really? Is English your first language? It is mine. I would never, ever, say 'We are going to finally win.' It's the most unnatural of the four. I'm glad it wasn't accepted. 'We are finally going to win' and 'Finally we are going to win' are both perfectly natural. One is no better than the other.