If the Jews had to get Pilate to sentence Jesus to death because only the Romans could impose the death sentence, how was Herod able to slaughter the innocents?

Suetonious wrote that the Romans so feared a prophesied king who would rule the world that when Herod notified the Emperor of that the Magi had come searching for the KING, the Emperor ordered that all babies born in the entire Roman Empire that year were to be put to death.

Herod was the only provincial ruler who did it.  The rest of the empire did not because they considered the law immoral because they believed in the right of the child to live.