He killed them so fast they couldn't keep up.
True that.
He eventually killed almost the entirety of the Old Bolsheviks, so that the only leaders left were those who had come up under his control.
It should be noted, as in this case, that most of the Old Bolsheviks pretty much deserved their fate for their crimes. There are no "good guys" in these power struggles.
Unfortunately, the power struggles always also result in murders of family members, including children, and other true innocents.