Was Jesus Buried on the Day of His Crucifixion

All the Gospels agree that on the day Jesus was crucified, Joseph of Arimathea asked Pilate for the body and took it from the cross to bury in a tomb.

What almost no one realizes is that this would have been unprecedented, so far as we know, in the Roman world, where part of the humiliation of crucifixion was for the corpse to be left on the cross to decompose and be ravaged by scavenging birds for days before being disposed of. 

Did the Romans make an exception for Jesus? Is that plausible? Or is the story of his burial by Joseph a later legend? This is obviously an issue of enormous significance. If Jesus was not buried that afternoon, how could he have emerged from the tomb "on the third day"?