Blackstock grabbed his third goal in three games to leave Alan Pardew’s side with no chance of reaching the play-offs.
The Addicks kicked off knowing only a win would keep their faint hopes alive, but instead they put in an error-strewn performance and looked beaten from the moment Blackstock’s 15th-minute effort hit the net.
So poor was their display, the travelling fans began ironically chanting ‘ole’ when they managed to string more than two passes together.
By contrast Rangers look a side destined for a bright future under owners, Bernie Ecclestone and Flavio Briatore.
Blackstock’s effort was enough after he expertly turned Paddy McCarthy before placing a left-footed shot past Nicky Weaver.