The Clarets bagged a late point thanks to Jordan Cropper’s 90th-minute penalty to move up a place to fourth spot in the U18 Professional Development League’s northern group.
Danny Cadamarteri’s side are still without a win since January but stopped Charlton’s winning streak to make it two games without defeat.
The in-form Addicks were on course for a seventh successive victory until Cropper (above) held his nerve to convert from the spot in a dramatic finale which also saw the dismissal of Clarets full-back Matthew Glennon.
Meanwhile, the Clarets’ Lancashire FA Professional Youth Cup semi-final at home to Wigan Athletic has been re-arranged for Tuesday, 3 April (KO 2pm).
The fixture was originally postponed on Tuesday, 27 February due to snow-covered pitches at the Barnfield Training Centre.
Burnley: King, Cropper, Glennon, Layton, Wilson, King, Jumeau (Ellison 57), Moss, Harris (Yari 75), Mupariwa (Blair ht), Barrett. Substitutes: Bruce, Mpofu.