They had to survive a few anxious moments in the closing stages as Charlton launched a late rally but the Addicks could not find a goal and slipped to within two points of the drop zone.
Reading went ahead early in the first half when Billy Sharp, making his full debut for the Berkshire club, drilled home a fine effort past goalkeeper Ben Alnwick.
Alex Pearce nodded over from a Danny Guthrie corner as Reading started the brighter but Charlton, who lost 1-0 at home to Ipswich on Saturday, perhaps should have had a penalty early on.
Reading keeper Alex McCarthy dithered and team-mate Stephen Kelly appeared to clip Simon Church, the former Reading striker, from behind.
Referee Darren Sheldrake waved play on, however, and Reading were quick to capitalise on their good fortune in the 13th minute.
Danny Williams gained possession in midfield and swiftly released Sharp. The on-loan Southampton striker took aim and beat Alnwick from 20 yards with a crisp shot for his first goal for the club.
Charlton offered little going forward and could have fallen further behind when Alnwick fumbled Pavel Pogrebnyak's 30-yard drive but the keeper recovered in time to block the onrushing Sharp.
The Addicks responded when Church raced clear of the home defence but McCarthy narrowed the angle and saved his effort.
Reading continued to dominate in the second half and almost doubled their lead soon after the restart. Garath McCleary homed in on the target but his well-struck 20-yard attempt struck a post and went behind.
Charlton at last got going but Dale Stephens failed to trouble McCarthy with a poor long-distance effort.
The game entered a dull phase midway through the second period, with neither side able to muster any worthy goal opportunities.
Rhoys Wiggins wasted a decent chance, prompting Charlton manager Chris Powell to make a triple substitution, with Johnnie Jackson, Danny Green and Marvin Sordell all coming on.
It had the desired effect, with Charlton immediately looking far more dangerous.
Reading lost control of the midfield and were forced to backtrack furiously as Charlton drove forward with purpose but they could not make their superiority count with Sordell having a goal disallowed for offside and Jackson and Cameron Stewart wasting efforts.