The Addicks dominated possession throughout the tie at Underhill and Johnnie Jackson should have given them an early but he dragged his shot wastefully wide.
Barnet regularly found themselves penned into their own half and Jackson again went close in the 20th minute with a 25 yard free-kick.
The hosts' first real opportunity came after 38 minutes when Mark Marshall, who was a threat throughout, drove in a cross from the left that Rob Elliot flapped at before Matt Fry bravely cleared.
Charlton came close to scoring after 65 minutes when replacement Pawel Abbott hit the bar with a flicked header from Scott Wagstaff's cross.
A long spell of Charlton pressure saw Therry Racon fire narrowly wide after 68 minutes before Benson then did the same when clean though two minutes later, but Barnet threatened late on and Elliot twice denied Marshall with fingertip saves in the last 10 minutes.