Who Actually Won the Space Race?

All these years later, people (in America at least) know the U.S. won the space race. I mean, we landed on the moon. But, if you think about it, did did the U.S. really win the race? Because the Soviet Union was first in space in pretty much everything except for the moon. First satellite, dog, man, and woman (in that order) in space.

So, who actually won?