Chris Powell's freefalling side looked destined for a fourth straight defeat after Andy Reid's early strike against his old club.
But Sordell, on loan from Bolton, levelled just after the interval to secure a much-needed point for the Addicks.
Reid took just two minutes to find the net on his old stomping ground after Jordan Cousins fouled him on the right edge of the penalty area.
The Valley faithful knew what to expect as Reid stood over the free-kick - he had scored plenty during a successful 18-month spell with Charlton five years ago - and he did disappoint them.
The angle was a tight one but Reid curled his effort over Addicks keeper Ben Hamer and inside the far post for his fifth goal of the season.
Charlton had plenty of chances to recover from that early blow during the first half but the ball would not break for them in front of goal.
Twice left-back Rhoys Wiggins overlapped and fired in dangerous low crosses but close-range efforts from Simon Church and Sordell were deflected clear.
Sordell also had a goalbound shot blocked by Chris Cohen and Lawrie Wilson's charge through the centre ended when his drive flew narrowly wide.
Forest could have been two up by then, however, after Jamie Mackie raced through and saw his initial shot blocked by Hamer eight yards out.
The ball cannoned back off the Scottish forward and was bouncing towards goal until Wilson got back in time to hook it off the line.
Forest had a double let-off just before the break when keeper Karl Darlow parried Dale Stephens' shot to the feet of Church but once again the striker could not take advantage.
The ball eventually fell back to Stephens who lashed his shot just over the crossbar from 15 yards out.
But Charlton's luck in front of goal finally changed five minutes into the second half.
A half-clearance from Forest fell to Wilson out on the right and he fizzed a low cross towards Sordell who swept it first time past Darlow and into the net.
From then on Charlton looked the likelier winners, and they came closest when Cousins crashed a volley against the outside of post, while skipper Michael Morrison blazed over from six yards in stoppage time.