The Addicks recorded their third successive draw at The Valley after a 1-1 stalemate with Birmingham on Saturday.
Chris Solly returned at right-back and Michael Morrison came in for the unavailable Tal Ben Haim.
George Tucudean recovered from his back problem and was included on the bench.
Young central defender, Terell Thomas, was included in the squad for the first time.
The Addicks started brightly and in the third minute, Igor Vetokele fired across goal, but his shot went narrowly wide of the far post.
Vetokele did not have to wait long for another opportunity and this time he made no mistake. A peach of a cross from Frederic Bulot on the left, gave the unmarked striker the simple task of heading past Randolph to give Charlton the lead.
The Blues then came into the game more and Clayton Donaldson spurned a glorious opportunity, after Yoni Buyens lost the ball in midfield.
The visitors did get the ball in the net after 34 minutes but the goal was disallowed for offside, Donaldson touching it in on the line.
The Addicks again started brightly after the interval and Vetokele played the ball across to Lawrie Wilson who curled a left-footed effort just over.
The Blues started to create chances too and it needed a great save from Stephen Henderson to foil Paul Robinson.
The visitors did restore parity after 53 minutes though. A clever routine from a corner saw David Davis swivel and fire a left-foot shot past Henderson’s despairing drive from 20 yards.
Both sides had chances to win, Solly made a buccaneering run but could not find a finish.
The game had a worrying end when Jordan Cousins landed awkwardly and had to be stretchered off encased in a neck brace.
There is now a two week break until the game at Bournemouth. Charlton will not face former talisman, Yann Kermorgant, after the Frenchman was red carded for a horrible looking challenge at Bolton.
Bob Peeters will need to assess his squad’s injury situation and decide whether reinforcements are needed.
Charlton: Henderson; Solly, Morrison, Bikey, Wiggins; Wilson (Tucudean 70), Buyens, Cousins (Fox 90), Jackson (Moussa 58), Bulot; Vetokele.
Subs (not used): Pope, Thomas, Harriott, Ahearne-Grant.
Goal: Vetokele 11
Birmingham City: Randolph; Grounds, Robinson, Edgar, Caddis; Davis, Reilly (Gray 65), Cotterill, Gleeson, Arthur (Thomas 79); Donaldson.
Subs (not used): Doyle, Packwood, Hall, Johnstone, Lee.
Goal: Davis 53
Booked: Gleeson 75 (foul).
Referee: Paul Tierney (Lancashire).
Attn: 16,369 (1,500 Birmingham).