The better translation for this meaning would be "Greece (won against)/(beat) Spain yesterday." The phrase "won over" is a correct literal translation but in English means to convince someone of something.
It can technically have the intended meaning, but would tend to have a comma, or a some kinda of short pause in speech.
Greece won, over Spain, yesterday.
"Won over" sounds equally natural to "won against" to me for that meaning. It's just that "won over" is ambiguous without context.
and what about "won from" ? instead of won over ?
No, "won from" does not work in English. "Won against" is the best choice.