Goals from Jobi McAnuff and Andy Johnson pushed Palace firmly among the play-off contenders, while Craig Levein's Leicester are now facing a battle against the drop.
Dowie has not ruled out catching second-placed Sheffield United and an extended good run in the new year could just see Palace ruffle a few feathers.
The first half never really got going although a couple of chances were on offer at both ends.
On 10 minutes Clinton Morrison forced a reflex save from City keeper Rab Douglas after a tremendous cross from Johnson on the right flank.
Then Johnson again caused mayhem, this time crossing for Ben Watson, who could only fire over the target.
Otherwise the Foxes held their own and perhaps were worth a goal, with an Iain Hume header going just wide.
The second half was a different story with home shot-stopper Gabor Kiraly totally unemployed, but at one stage it looked as if the Foxes would hold out.
Johnson saw a penalty saved by Douglas after Patrick McCarthy handled with only 15 minutes left. It was a rare spot-kick miss by Johnson, but credit must go to the Scottish keeper who guessed correctly by diving to the right.
However, the Eagles' next attack saw the breakthrough finally arrive.
Substitute Dougie Freedman performed an amazing run along the right byline before crossing into the goalmouth for McAnuff to stab home from just six yards out.
In stoppage-time Johnson took the match beyond Leicester's reach, as Mikele Leigertwood smartly broke up a City attack and then sent the striker clear to tap the ball under Douglas' body for the eighth goal of the season.