Palace started the game brightly, forcing two saves from Leeds keeper Andy Lonergan in the opening minutes through Chris Martin and Jermaine Easter, before the former gave the Eagles the lead.
The Palace hitman drilled his shot low and out of the clutches of Lonergan to give his side a sixth minute lead.
The hosts continued to push on, with Darren Ambrose hitting a ferocious strike just over the crossbar.
As Leeds began to edge themselves more into the match they started to create more chances, with Ross McCormack almost profiting on a defence-splitting pass, only for Julian Speroni to deny him.
Speroni was in fine form later too, first clawing away an effort from Adam Clayton before smothering Tom Lees from close range.
Palace hit back with a chance of their own through Martin, but the striker should have done better with only Lonergan to beat.
The hosts were handed a blow on the stroke of half time, however, when Sean Scannell was shown a second yellow card for a foul on Danny Pugh, reducing the Eagles to ten men.
Leeds looked to capitalise on their extra man earlier in the second half with an effort from Lees, but once again Speroni was equal to it.
Simon Grayson then decided it was time for a change for the visitors, bringing on Robert Snodgrass in place of Aidy White, and it proved to be an inspired substitution when Snodgrass swept Leeds level just after the hour mark.
The Whites began to press the ten men of Palace for a goal to put them ahead, and Snodgrass once again came close, as did Pugh, whose shot flew narrowly wide.