Malbranque slotted home from the penalty spot after Luis Boa Morte was brought down by Dean Kiely on 20 minutes with Davis sealing the win with a superb volley just after the hour mark.
The match began at a frantic pace at Loftus Road with both sides pushing numbers forward that created an exciting and open encounter.
Firstly, Edwin Van der Sar had to get down low to block Claus Jensen's drive while at the other end Boa Morte saw his shot flash just past the upright.
Graham Stuart was inches from beating the Dutch shot-stopper, but his left-footed effort drifted just wide of Van der Sar's right-hand post.
Sylvain Legwinski stopped a certain goal after nine minutes when he tracked Paul Konchesky's run to block a cross with the former Spurs man waiting to pounce in front of goal.
Moments after Legwinski headed over from Malbranque's left wing corner The Cottagers went ahead, with Chris Coleman's side again benefiting from Boa Morte's pace.
The former Arsenal and Southampton man just reached the ball ahead of Kiely in the penalty area leaving referee Matt Messias no option but to point to the spot.
Malbranque made no mistake from the ensuing spot-kick rolling his right-footed effort past the helpless former Republic of Ireland international.
Charlton almost had a penalty of their own shortly after, however Messias failed to award a penalty when Luke Young's cross was deflected out for a corner by Martin Djetou's hands.
Malbranque then drilled a dangerous free-kick just wide of Kiely's goal, but the keeper was involved shortly after when he was called upon to stop the Frenchman's shot after he skipped past three defenders.
The Addicks were denied another penalty when Alain Goma hauled down Jason Euell, while things got tasty in the middle of the park when Legwinski took offence to Stuart's late tackle.
The second half began as the first started with both sides surging forward and Charlton almost levelled, but with the ball bouncing around in Fulham's box no one was able to stab home.
Boa Morte burst away in trademark fashion and only a foul from full back Chris Powell could halt his run. The former England international was shown a yellow card for the challenge on the Portuguese winger.
With Charlton looking the more likely to score Davis collected Boa Morte's pass, but controlled poorly, however the ball floated into the air and he volleyed past the helpless Kiely from 25-yards.
Davis, who clearly gained confidence from his goal, tried his luck again from distance, but this time Kiely was on hand to block his shot before the rebound was hooked away from danger.
Euell should have pulled one back late on, but with a free header at the far post the former Wimbledon man failed to hit the target from a right-wing corner.
Despite Charlton playing with purpose and endeavour Van der Sar proved unbeatable on the day and Fulham ran out worthy winners and are now a point clear of Birmingham City.