Danny Haynes scored his third goal in as many games as in-form Charlton overcame Burnley at Turf Moor.
Midfielder Haynes pounced following Rob Hulse's second-half knock down after Burnley's Kieran Trippier had been sent off.
Trippier was shown a straight red after just 15 minutes when he was judged to have handled on the goal-line during a penalty box scramble.
Clarets keeper Lee Grant denied Johnnie Jackson from the resulting penalty.
Three in a row for Charlton
The last time Charlton won three second-tier league games in a row was November 2007, when they enjoyed a four-match winning run before losing at home to Sheffield United.
Charlton have now won their last three league games - their most successful sequence at this level for five years.
A spirited Burnley created enough chances to have secured at least a point but were wasteful.
Charlie Austin collected his Championship player of the month award on the pitch before kick-off and almost added to his 20-goal haul in the 12th minute, heading Trippier's cross over the angle of post and bar.
But Trippier lasted a few more minutes before he was dismissed soon after Charlton full-back Chris Solly had rattled the post.
Grant superbly turned Jackson's spot-kick around the post but Charlton continued to threaten, with Haynes slicing an 18th-minute volley wide.
The 10 men were almost ahead after the half hour through Brian Stock's rasping 30-yard shot before Michael Duff was also denied.
But Charlton secured the points when Hulse headed back across goal to leave former Ipswich player Haynes with a simple finish.
Burnley boss Sean Dyche:
"I think the sending off is difficult. I've seen it again and it looks like the ball has hit him rather than him hit the ball. But what can you do?
"It's a tough call and you get away with some but we didn't. Referees have a tough job to do but we probably haven't had our fair balance over the last couple of weeks. You hope that evens itself out over the season.
"We created a number of chances and took on the game with 10 men. The result doesn't always match the reality of the game and that was the case."
Charlton manager Chris Powell:
"It's a real tough place to come and they have been doing very well at home since Sean Dyche came in, so we knew it would be a tough game.
"We've come away from a hard-fought game, with some contentious issues, and got the three points which you have got to do in the Championship. It is quite an unforgiving league but we are in a good place at the moment.
"It was a well-worked goal and we had to be professional and see the game out. I thought we did that and we got the clean sheet which was pleasing."
Dorian Dervite is adjudged to have handled the ball. Free kick crossed right-footed by Brian Stock, clearance made by Bradley Pritchard.
Ricardo Fuller is ruled offside. Free kick taken by Lee Grant.
Free kick awarded for a foul by Brian Stock on Ricardo Fuller. Free kick taken by Daniel Seaborne.
90:00 +1:41 Substitution
Substitution (Charlton) makes a substitution, with Matthew Taylor coming on for Robert Hulse.
Dorian Dervite takes a shot. Blocked by Michael Duff.
Charlie Austin takes a shot. Ben Hamer makes a save.
Danny Ings sends in a cross.
Free kick taken by Brian Stock.
Substitution Dorian Dervite joins the action as a substitute, replacing Danny Haynes.
Free kick awarded for an unfair challenge on Charlie Austin by Leon Cort.
Brian Stock takes the outswinging corner, Charlie Austin takes a shot. Save made by Ben Hamer.
Direct free kick taken by Ben Hamer.
Substitution Sam Vokes replaces Martin Paterson.
Brian Stock gives away a free kick for an unfair challenge on Danny Haynes. Chris Solly restarts play with the free kick. The referee penalises Danny Haynes for handball. Free kick taken by Lee Grant. Charlie Austin challenges Salim Kerkar unfairly and gives away a free kick.
Brian Stock takes the free kick. Chris Solly concedes a free kick for a foul on Brian Stock. The free kick is delivered left-footed by Brian Stock from left wing, save made by Ben Hamer.
Booking Johnnie Jackson goes into the book.
Free kick awarded for a foul by Johnnie Jackson on Brian Stock.
Corner taken by Brian Stock from the right by-line.
Substitution Danny Lafferty goes off and David Edgar comes on.
Corner taken right-footed by Brian Stock from the left by-line, Danny Ings challenges Danny Haynes unfairly and gives away a free kick. Ben Hamer takes the direct free kick.
Substitution Danny Ings replaces Junior Stanislas.
The referee blows for offside against Danny Haynes. Lee Grant takes the indirect free kick.
Assist on the goal came from Robert Hulse.
68:45 Goal scored
Goal! - Danny Haynes - Burnley 0 - 1 Charlton Danny Haynes finds the net with a headed goal from inside the penalty area. Burnley 0-1 Charlton.
Michael Duff fouled by Robert Hulse, the ref awards a free kick. Direct free kick taken by Lee Grant.
Shot from just outside the box by Brian Stock goes over the bar.
Jason Shackell fouled by Ricardo Fuller, the ref awards a free kick. Free kick taken by Danny Lafferty.
Robert Hulse takes a shot. Save made by Lee Grant.
Foul by Ricardo Fuller on Dean Marney, free kick awarded. Free kick taken by Lee Grant.
Free kick awarded for an unfair challenge on Ricardo Fuller by Dean Marney. Johnnie Jackson takes the direct free kick.
Headed effort from inside the area by Charlie Austin misses to the left of the goal.
Junior Stanislas takes the inswinging corner, Header from close in by Jason Shackell misses to the right of the target.
Charlie Austin has an effort at goal from the edge of the area that misses to the right of the target.
Outswinging corner taken from the left by-line by Salim Kerkar, clearance made by Brian Stock.
Corner from the right by-line taken by Johnnie Jackson, Michael Duff manages to make a clearance.
Corner taken by Junior Stanislas from the left by-line played to the near post, Johnnie Jackson makes a clearance.
The referee gets the second half started.
45:00 +3:07 Half time
Half Time The players leave the pitch at half time.
Robert Hulse takes a shot. Leon Cort has an effort at goal from outside the area which goes wide left of the target. Jason Shackell makes a clearance.
Inswinging corner taken left-footed by Salim Kerkar from the right by-line, clearance made by Jason Shackell.
Corner taken by Salim Kerkar from the right by-line, save made by Lee Grant.
Free kick awarded for a foul by Eggert Jonsson on Charlie Austin. Free kick taken by Michael Duff.
Danny Haynes has a headed effort at goal from close range which goes wide of the left-hand post.
Robert Hulse gives away a free kick for an unfair challenge on Jason Shackell. Michael Duff takes the direct free kick.
Corner taken left-footed by Johnnie Jackson from the right by-line, Unfair challenge on Jason Shackell by Leon Cort results in a free kick. Direct free kick taken by Lee Grant.
Danny Haynes takes a shot. Save by Ben Hamer.
Johnnie Jackson concedes a free kick for a foul on Brian Stock. Free kick taken by Jason Shackell.
The ball is crossed by Junior Stanislas, save by Ben Hamer.
Bradley Pritchard takes a shot from just outside the penalty area which clears the crossbar.
Corner taken by Johnnie Jackson, Charlie Austin makes a clearance.
Inswinging corner taken right-footed by Junior Stanislas from the left by-line, Michael Duff takes a shot. Ben Hamer makes a save. Corner taken by Junior Stanislas from the right by-line, clearance made by Michael Morrison.
Brian Stock takes a shot. Save by Ben Hamer.
Eggert Jonsson gives away a free kick for an unfair challenge on Chris McCann. Junior Stanislas crosses the ball in from the free kick, Ben Hamer manages to make a clearance.
The assistant referee signals for offside against Danny Haynes. Jason Shackell takes the free kick.
The ball is crossed by Salim Kerkar.
Free kick awarded for a foul by Brian Stock on Robert Hulse. The free kick is delivered left-footed by Daniel Seaborne from left wing, Michael Duff makes a clearance.
Martin Paterson is caught offside. Indirect free kick taken by Ben Hamer.
Bradley Pritchard concedes a free kick for a foul on Chris McCann. Brian Stock takes the free kick.
Martin Paterson takes a shot. Ben Hamer makes a save.
Johnnie Jackson handles the ball and concedes a free kick. Junior Stanislas delivers the ball from the free kick right-footed from right wing, clearance by Bradley Pritchard.
Shot from just outside the area by Martin Paterson misses to the right of the target.
Daniel Seaborne challenges Junior Stanislas unfairly and gives away a free kick. The free kick is swung in right-footed by Junior Stanislas, Eggert Jonsson makes a clearance.
Effort from deep inside the area by Danny Haynes misses to the left of the goal.
Free kick awarded for a foul by Chris McCann on Salim Kerkar. Johnnie Jackson restarts play with the free kick.
Outswinging corner taken left-footed by Salim Kerkar from the left by-line, Leon Cort challenges Michael Duff unfairly and gives away a free kick. Lee Grant takes the direct free kick.
Penalty taken by Johnnie Jackson saved by Lee Grant. Burnley 0-0 Charlton.
Dismissal The referee shows Kieran Trippier a red card.
Handball decision goes against Kieran Trippier.
Charlie Austin has a headed effort at goal from deep inside the area missing to the left of the target.
Corner taken by Junior Stanislas, clearance made by Leon Cort.
Danny Haynes takes a shot. Save by Lee Grant.
Shot from just outside the box by Chris McCann goes over the bar.
Free kick awarded for a foul by Eggert Jonsson on Martin Paterson. Jason Shackell takes the direct free kick.
The assistant referee signals for offside against Danny Haynes. Lee Grant takes the free kick.
Michael Morrison fouled by Dean Marney, the ref awards a free kick. Direct free kick taken by Michael Morrison.
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