Midfielder Wade Elliott hit a stunning second-half shot to keep Burnley on the fringes of the play-off positions and dent Charlton's promotion hopes.
Robbie Blake slipped the ball into the path of the onrushing midfielder, who thumped an unstoppable left-foot drive into the top-right corner of the net.
Burnley were the better team and left-back Jon Harley's crosses created a number of chances.
Darren Ambrose, Sam Sodje and Leroy Lita all missed chances for Charlton.
Burnley manager Owen Coyle:
"I thought the goal was worthy of winning any game, not just the finish but also the build-up play.
"It's what we're getting known for and that's what we want, a bit of style about our play, getting the ball down and passing and moving.
"The goal was well worth the admission money alone I reckon."
Charlton boss Alan Pardew:
"We're very disappointed as we felt we played a very good game - it was an absolute wonder goal when we were in total control.
"We just need a break and I think we deserve a break. If they play with that level of commitment we'll be OK.
"I thought we were unlucky, but the performance will make us stronger."
Burnley: Kiraly, Alexander, Carlisle, Varga, Harley, Elliott, James O'Connor, Mahon (Spicer 63), Lafferty, Cole (Akinbiyi 75), Blake (Randall 87).
Subs Not Used: Jensen, Unsworth.
Goals: Elliott 59.
Charlton: Weaver, Halford, Sodje, McCarthy, Thatcher, Semedo (Zhi 79), Holland, Thomas, Ambrose (Varney 69), Gray (Iwelumo 69), Lita.
Subs Not Used: Elliot, Fortune.
Ref: Phil Joslin (Nottinghamshire).