Ironically after Daniel Farke fielded an attacking line-up it was a controlled defensive performance that earned the draw after Gabriel Gudmundsson’s dismissal just before half-time after the Whites missed a penalty.
In a match low on quality at a windswept Selhurst Park, Leeds had to dig deep with Joe Rodon outstanding at the heart of the United backline and skipper Ethan Ampadu disrupting Palace in midfield leaving goalkeeper Karl Darlow with very little to do.
United had the better of the early chances with Brenden Aaronson missing a decent opening before Palace keeper Walter Benitez came extremely close to carrying a Dominic Calvert-Lewin over his line.
A drab encounter, in which the Whites were marginally the better of two sides struggling in the blustery wind, burst into life just before the interval.
Leeds, who played strikers Calvert-Lewin and Lukas Nmecha together for the first time since early December, gained a corner after 43 minutes when Will Hughes handled in the box.
Calvert-Lewin stepped up, sent Benitez the wrong way but screwed his kick wide of the post.
Moments later Jaka Bijol, already booked, escaped a second yellow when he fouled Ismaila Sarr although both managers received cautions for over expressing their views on the incident.
The drama was not over. The game had barely restarted after Sarr received treatment when referee Thomas Bramall booked Gudmundsson, who had earlier been carded for a foul on Brennan Johnson, but the official had appeared to have forgotten and took an age to show the Swede red.
Leeds boss Daniel Farke withdrew Nmecha and Brenden Aaronson at half-time and went with a 5-3-1 formation with Jayden Bogle coming on and James Justin switching defensive flanks while Illia Gruev was introduced to stiffen the midfield.
The message was clear. What we have - a point - we hold. Farke’s team executed his plan to perfection with sluggish Palace having little idea on who to break Leeds down.
There was just one moment of alarm for Leeds when Jefferson Lerma headed home after a stunning save by Darlow but Brennan Johnson, who initially delivered the ball into the box was offside.
The Leeds contingent thought Gudmundsson’s second booking was harsh and also felt aggrieved 20 minutes from the end when Johnson, previously booked, escaped a second card for a clear trip.
Although he welcomed a point on the road, Farke probably knew it was an opportunity missed against an out-of-sorts Palace.
He said: “I would trust my lads with my life. We are not perfect, but the mentality in the dressing room is second to none. In the circumstances, in a difficult away game, we defended the whole time and we didn’t give any chances away,”
With fellow strugglers West Ham, Tottenham and Nottingham Forest also drawing at the weekend Leeds remain three points ahead of the drop zone with eight games remaining.