Having got out of the bottom three on goal difference after Friday's match at Manchester City, they have now moved a point ahead of Sheffield United and are now just two behind Wigan and three behind Fulham.
Reading provided tough opposition although they are now without a win in their last eight Premiership matches while Charlton's successful sequence of results has seen them win three and draw three and in five of those matches they have kept a clean sheet.
Reading made five changes from the side that lost to Liverpool on Saturday and Charlton just one, but manager Alan Pardew was forced into two more alterations inside the first half-hour as Hermann Hreidarsson and Marcus Bent both went off injured.
Charlton had a wonderful chance to take the lead after just five minutes when Darren Ambrose's free-kick found defender Talal El Karkouri six yards out with a free header.
It bounced off the under side of the crossbar and was cleared to safety but Reading hit back quickly and Ki-Hyeon Seol had an equally good opportunity when he was free on the Charlton goal.
However, Scott Carson managed to get the shot away and, just before the break, the Charlton keeper had to tip over a Steven Sidwell header.
In an open game it was amazing that the scoreline stayed goalless and Darren Bent was inches away from giving Charlton the lead whilseat the other end El Karkouri managed to clear Leroy Lita's header off the line.
Charlton made their third substitution when Kevin Lisbie replaced Alexandre Song Bilong but it was Reading who were more likely to score and the home side were fortunate when Stephen Hunt's header flew across the face of goal.
In a last-gasp effort to get the goal which would bring them a vital three points Charlton's Darren Bent fired across the face of goal and Ambrose saw his shot saved by Marcus Hahnemann.
A draw was probably a fair result and, with Sheffield United the next visitors to The Valley, Charlton's destiny is still very much in their own hands.
Reading can look back on a highly successful season which has hit the buffers in recent matches but still leaves them in a very healthy position.