Both sides had their share of possession in the early stages, but the struggling Addicts were first to threaten as Jonathan Obika came within inches of reaching Simon Church's cutback in front of goal.
Charlton almost took the lead in the 25th minute when Church latched onto a stray pass and bore down on goal, testing Burnley goalkeeper Tom Heaton with a stinging strike.
A forgettable first half had suddenly come to life, and the deadlock was broken seven minutes before the interval when Ashley Barnes headed home Junior Stanislas's cross to make it 1-0 to the visitors.
Charlton almost pulled one back in the 64th minute as Astrit Ajdarevic forced an impressive save out of Heaton with a bending free kick, the Burnley keeper getting down low to keep it out.
Jose Riga's side continued to press for a consolation goal in the dying stages, but it was Burnley who had the final say, with Michael Kightly adding a third in the final minute to add insult to injury.