After a promising start, Charlton's season appears to be falling apart. This was their third successive league defeat and their second at home in the space of five days.
Had Rangers taken their chances in the second half they would have won by a bigger margin, but the three points and the victory will boost caretaker manager Mick Harford's chances of getting the job on a permanent basis.
The visitors seemed to have blown their chances of victory on 50 minutes when Martin Rowlands put his penalty kick wide of Charlton goalkeeper Nicky Weaver but it hit the foot of the post and rebounded to safety.
The spot-kick had been awarded when Rowan Vine was brought down by Jonathan Fortune.
Weaver then had to block a shot on the line from Vine and Mikele Leigertwood then shot wide with only the goalkeeper to beat.
The winner came on 72 minutes when Charlton failed to clear a left-wing cross and Rangers skipper Adam Bolder fired the ball low into the net.
Charlton had a couple of good chances in the first half, Sam Sodje heading against the top of the crossbar and Luke Varney firing over.
After the break they became frustrated and were never able to get any kind of rhythm, with their only real chance of the half falling to Varney again and he saw his goal-bound shot well saved by goalkeeper Lee Camp.
The one bright spot from a disappointing Charlton display was a promising league debut for 18-year-old left back Grant Basey.