Scrum-half Youngs bagged his first try for his country as did Northampton wing Chris Ashton to help give England a 15-13 lead at the break.
Even after centre Matt Giteau grabbed his second try after the break, England did not buckle and penalties from Toby Flood and Jonny Wilkinson, hero of the 2003 triumph over the Wallabies in the same stadium, edged them back in front.
But there proved a dramatic twist, when Giteau - normally so reliable with the boot - missed one penalty from the touchline and then a regulation three-pointer in front of the posts as Martin Johnson enjoyed his greatest result as England manager.
Flood opened the scoring with an early penalty before Giteau, recalled to the side in place of Berrick Barnes, responded with two kicks of his own.
England though fashioned the game's first try in superb fashion. Flanker Tom Croft won lineout ball before feeding Leicester teammate Youngs who burst past Drew Mitchell and into the corner.
Flood converted put England 10-6 but the Wallabies hit back with a great score of their own as Quade Coope and Digby Iaone combined to put Giteau over.
Ashton was the next player to strike with Youngs turning provider before Tom Palmer offloaded for the winger to apply the finish.
England's narrow halftime lead was wiped out when a brilliant backline move put Giteau over who again converted his own score for a five-point lead.
That was narrowed by Flood who was soon replaced by Wilkinson who in turn struck to give England a narrow lead.
Giteau should have wiped that advantage out with two penalty misses - the first forgivable, the second inexcusable.
The jitters proved contagious as Wilkinson missed a late penalty to seal the win but it made no difference as the fly-half cleared the ball to seal only England's third defeat of the Wallabies on Australian soil.
Australia took the Cook Cup on aggregate but the celebrations firmly stayed in the England camp.