Leicester - who face Atletico Madrid in the second leg of their Champions League quarter-final on Tuesday - took an early lead through Robert Huth with Jamie Vardy adding a second early in the second half at Selhurst Park.
But Palace swiftly responded through Yohan Cabaye and Christian Benteke to secure a draw that took them up to 15th, seven points clear of the bottom three and within five of ninth.
Cabaye pulled one back within just two minutes and it fell to Benteke to head in the leveller, with Palace looking the more likely to seal a win late on, though Leicester held firm.
"We are going to give him every opportunity", interim manager Craig Shakespeare said, agreeing that Huth was huge and that the German's influence accentuates the need to get Morgan back.
It was at that moment where the game burst into life as Yohan Cabaye pulled one back nearly immediately, which rallied the home fams to push their team for an equaliser.
"It doesn't surprise me [that Palace are doing well under Sam Allardyce] having worked with Sam for a very short space of time [at England]".
Leicester left-back Christian Fuchs directed his throw from the left wing into the heart of the Palace area where Huth rose above Joel Ward to direct his header past keeper Wayne Hennessey from six yards.
Nigerian midfielder, Wilfred Ndidi, was impressive for Leicester City in the 2-2 draw with Crystal Palace at Selhurst Park on Saturday.
Leicester boss Craig Shakespeare, meanwhile, struggled to hide his disappointment after his side failed to hold on to their lead.
Again Palace did not lose belief, and within two minutes scored their first goal. "We need to concentrate on Palace and try to get those points", he said. "On reflection, when you finish a game with a point having been 2-0 down, you have to be incredibly satisfied with that point".
"We showed good character to get back into the game, but it is mixed feelings for us really". But we must keep picking up points until we're safe.
Yohan Cabaye netted his team's first before Benteke completed the comeback in the 70th minute, with neither side able to find a victor. Their wingers, we need to keep them quiet and then the threat of Benteke in the air too.