Everton defender Joleon Lescott had equalised deep into stoppage time but after taunting the away support, the former Wolves defender lost his concentration and Young took full advantage.
The flying winger ran the length of the pitch to celebrate with a set of Villa fans who been left in despair just a minute earlier.
Steve Sidwell had given Villa the lead inside the first minute with a rasping drive after James Milner's lay-off. Everton then began to press and Lescott took advantage of poor defending to restore parity.
The away side then survived a few scares to go in level at the break. They emerged stronger and began to fight back against Everton's midfield dominance.
Villa were soon given an early Christmas gift by Everton as Phil Jagielka played an horrendous backpass which Young gratefully latched onto. The England starlet curled the ball past Tim Howard effortlessly and the Villans had something to defend.
They looked to have completed their job as Joseph Yobo headed wide with a minute of stoppage time remaining and the fans celebrated what they thought was a victory.
Lionheart
But, Lescott volleyed home acrobatically after Jagielka headed the ball in his direction and the travelling support was left shattered.
Some fans may have considered leaving but were too stunned to do so and with Villa about to kick off it looked certain that Lescott's goal would be the last meaningful touch of the ball.
But, referee Martin Atkinson, who had a fine game, allowed enough time for Howard to clear the ball into the Villa half.
Martin Laursen headed away in powerful fashion and Steven Pienaar failed to control leaving, which gave Gabby Agbonlahor possession.
The speedy striker prodded the ball to Young who darted past Lescott and fired emphatically past the American keeper.
Villa were jubilant and at the final whistle the players couldn't wait to enjoy the moment with their adoring fans.
Martin Laursen looked as stunned as anyone as he threw his shirt into the crowd and he deserves immeasurable plaudits after a lionheart display.
Young was congratulated by his manager, who looked like he was about to propose right there on the pitch.
It was a great day for all involved with the club and it is a day that most Villa fans and players may never forget.