The gap between Kevin Blackwell's side and Sheffield United is getting closer and a dogged performance at Palace suggests they are well prepared for the important run in.
Robbie Blake fired Leeds ahead on 33 minutes and Rob Hulse added a second eight minutes after the interval.
Then they defended, leaving Palace just the scraps to work on with Jobi McAnuff eventually scoring in stoppage time, but it was all too little too late.
United made a good start and would have taken the lead on six minutes but for a brilliant save from Gabor Kiraly in the Palace goal.
Gary Kelly's perfect corner was met by Paul Butler who got in a powerful header but the Hungarian keeper amazingly kept the ball out.
Livewire Eddie Lewis volleyed into the side netting at Leeds stepped up the pressure.
Although McAnuff and Darren Ward had useful headers, it was Leeds who made the breakthrough on 33 minutes.
Hulse held up the ball for Liam Miller who somehow managed to deliver a low cross into the goalmouth allowing Blake to score with the simplest of tap-ins.
Eight minutes after the break Leeds doubled their lead with Miller the provider once again.
From the right he crossed low and Hulse was on the spot five yards out to react with a rising shot which seemed to strike the underside of the bar before going over the line.
It certainly proved a killer goal as Palace lost their way as they struggled on a difficult surface.
It took an hour before Palace tested Neil Sullivan with Mikele Leigertwood unleashing a tremendous volley from 30 yards.
It proved the start of a good spell from Palace and Sullivan was again called upon to make a goalline save following a real scramble where any one of five Palace players could have forced the ball over the line.
Sullivan then saved a low shot from Micheal Hughes followed by Leigertwood shooting just wide.
Andy Johnson blasted over the bar and Gary Borrowdale crafted a good chance which went wide but the Eagles kept plugging away and eventually pulled one back in the first of four minutes of stoppage time.
Johnson found McAnuff who drifted cleverly into the area before firing past Sullivan and into the top corner.
But it was too little and too late and for Leeds the three important points has put them into the top three.