It was an unlikely point as Leicester - chasing a seventh straight win - looked comfortable for most of the match, but they paid the price for trying to sit on a narrow lead.
Grayson was nearly given the perfect start when Dave Martin dropped the ball at the feet of Luciano Becchio but the Leeds striker thumped his shot against the post from four yards.
Leicester were playing the better football and gained their reward in the 24th minute when Matt Fryatt broke across the front of the area and fed Matt Oakley who drove his shot across the face of Casper Ankergren.
There was little to excite the 33,580 crowd on Boxing Day with both sides giving away the ball and very little goalmouth incident although Becchio did squander a second chance when put through by Robinson.
The match looked to be petering out until Snodgrass seized on a perfect chip by Jonny Howson and forced it in at the far post.