If we were talking the first successful lunar probes
Then that would indeed have to go to the Soviets. But I wasn't. :^)
Note that from Sven's site which Raoul linked to the Soviets had planned to launch
their first lunar probe just one day after Pioneer 0's actual launch, but it was postponed
to that fall - and failed anyway.
Let us just be happy that the attempt was made in our era of human history and
that we have sent probes into space and we will hopefully see a permanent presence
on the Moon and Mars (and NEOs) in our lifetimes.
And maybe a starprobe.