The Scot popped up at the far post in injury time to force home Jonny Howson's chip and send the Leeds fans home happy.
It was a blow for Leicester City, who dominated most of the game without being at their best, but perhaps they will reflect they shouldn't have sat back so much against a frail Leeds defence.
Grayson made five changes from Gary McAllister's final team including bringing back Andy Robinson and leading scorer Jermaine Beckford following their hamstring injuries.
Nigel Pearson had the luxury of an unchanged side as confident Leicester went looking for their seventh straight win.
Leicester looked comfortable going forward but the first real chance fell to Leeds. Dave Martin dropped a cross under pressure from David Prutton and Luciano Becchio hit a snap shot from inside the six-yard box that cracked back from the post.
It was a gilt-edged chance and Leeds paid the price after 24 minutes when a slick Leicester move saw them go in front.
Steve Howard's power won a header, Matt Fryatt broke into midfield, drawing defenders towards him before laying it of to skipper Matt Oakley who drove it past Casper Ankergren.
Suddenly all the recent Leeds' frailties were apparent again, especially at the back where Fryatt was causing plenty of problems.
Leeds were on defence most of the time and had to make do with a long-range effort from Frazer Richardson and a second good chance for Becchio, who was put through by Robinson but completely mis-hit his shot.
Given their recent form, Leicester were struggling to dominate, some of their play rather casual and sloppy. But they never really looked under too much pressure and seemed comfortable just to consolidate their one-goal lead.
Until Snodgrass made them pay the price.