The visitors carried little threat from an attacking perspective but dealt with everything that came their way to distend the gap between themselves and the relegation zone to five points.
Conor Gallagher also saw his audacious half-volley from the edge of the area blaze over the crossbar, and just in the last 10 minutes alone, Palace had two attempts blocked - handing Jesse Marsch and his defence a second successive clean sheet.
Story of the match
Coming into the game with the desire to put three consecutive defeats behind him, Patrick Vieira named a greatly different starting eleven on Monday night.
As for Leeds, Dan James was used as their lone striker, with Raphinha, Jack Harrison, and Rodrigo just behind.
Incipiently, the game showed signs of an unhinged tempo, giving way for both sides to find space on the pitch, but both attacks found it difficult to find the all-important goals to seal three points.
Early in the first half, Jean-Phillipe Mateta beat Meslier to the ball following Leeds' failure to deal with a pass forward to the Frenchman, but the Palace favourite failed to get enough purchase on his shot to avoid a Llorente clearance.
Mateta was subject to a plethora of chances in the opening half, and he found himself cutting a frustrated figure in front of the goal again when Ayew's cross from the right met the Frenchman's head, but the striker once again couldn't find the net.
While Palace continued to probe the Leeds backline, finding little to no conviction in their final attempts, the visitors' only attempt on target in the first 45 minutes saw Cooper's tame header at the back post dealt with ease.
As fuel for the game continued to gather on the pitch throughout the first half, it soon turned to fire in the dying embers of the first period.
The polarised nature of Wilfried Zaha's personality saw his temper get the better of him as he seemingly pushed Raphinha in the face. The Ivorian avoided a booking, but Joachim Andersen brandished a yellow card for his forthcoming late challenge on Rodrigo.
The bad-tempered affairs that were forged in the latter stages of the first half continued at the start of the second period. A dangerous, sliding tackle that Dan James performed on Joel Ward sparked further fury towards the opposition and referee for Palace.
As the game got to boiling point, with some curious decisions being made by the officials, the spectators that had crammed themselves into Selhurst Park feared the game would fade into nonexistence - but The Eagles kept going forward.
Jean-Phillipe Mateta was the subject of desperate sighs from the Holmesdale End as the Frenchman failed to make amends for earlier misses by continuing the trend of doing everything right until the finish.
The attacking demeanour of Olise caused problems for the left side of Leeds' defence, and while the display through the entire game was wholly dominant, it was the last 10 minutes that proved to be one-way traffic the most.
Zaha's last-ditch attempt in stoppage time saw it deflect agonisingly over, leaving the game goalless. Despite momentum on their side for the majority of the game, Patrick Vieira's team were left to rue their missed chances.