Liverpool defender Daniel Agger headed the hosts in front after just seven minutes but Darren Bent pounced on Theo Walcott's low cross to haul England level just three minutes later.
The second half was littered with substitutions, and Young - one of England's replacements - grabbed the winner in the 68th minute after taking Glen Johnson's pass in his stride before finishing coolly inside Thomas Sorensen's near post.
All eyes were on Jack Wilshere on the Arsenal youngster's first full international start, and while the midfielder looked comfortable-if-unspectacular in a deep-lying role, his 45-minute contribution was outshone by that of fellow youngster Christian Eriksen in the Danish team.
The first-half show was stolen by a player six weeks younger than Wilshere, someone the Danes like to acclaim as the new Michael Laudrup and someone who looks sure to have a big future in front of him.
The youngest player to be named in any of the 32 World Cup squads, Eriksen caused devastation in front of an England back-four Wilshere was trying to shield.
His efficiency of movement allowed the Ajax player to find space with unerring regularity, from which he tended to leave the England defence anxious and despairing in equal measure.
Eriksen created an early opportunity for Nicklas Bendtner, had a shot deflected wide by Frank Lampard and slammed a quite brilliant effort against the base of Joe Hart's left-hand post.
It was hardly a surprise Eriksen should claim the assist for Denmark's early opener too.
As this was a warm-up for next month's Euro 2012 qualifier with Wales, Fabio Capello could not have been happy with the ease Denmark opened the scoring.
Eriksen's brilliant curling cross was difficult to defend. Nevertheless, Lampard and John Terry would be disappointed Agger had so much space to steer the ball beyond Hart's despairing grasp.
England did well to get themselves back on terms so quickly.
Capello had already acknowledged the work Rooney has done at Manchester United this season creating opportunities for others.
It was Rooney's excellent pass that offered Theo Walcott the room to run, crossing low to the far post for Bent to tap home his second international goal.
Bent had a second disallowed for offside shortly before the interval, although that would have been tough luck on the Danes given England's only other chance of note was a Rooney effort that Mathias Jorgensen booted off the line when the game was still goalless.
Capello made half of his six changes at the break, including the departures of both Wilshere and Lampard, who like his midfield partner did not make a significant contribution, and the long-awaited re-appearance of Scott Parker after an international absence of almost four and a half years; the first player to win his first four England caps while with four different clubs.
It also led to Ashley Cole taking the captain's armband as he won his 87th cap, a record for a full-back, completing a remarkable few days for the 30-year-old, who was named England's player of 2010 on Monday.
Eriksen looks as though he will be named Denmark's equivalent on a few occasions.
Although the second half was largely a sterile affair, Eriksen provided a moment of genius as he checked inside Glen Johnson and cut into the box.
Fortunately for England, the cross did not match his earlier work.
Of those in white, Bent was impressing. He could not get the ball into the Denmark net when he went face to face with Thomas Sorensen in a bid to reach Young's cross before racing on to James Milner's through ball and blasting narrowly wide.
But it was Young who got the second, striding through confidently after Johnson had won possession just inside the Denmark half, then beating Sorensen with a neat, low finish.
It was the Aston Villa man's first international goal and the highlight of a decent display for Young, a direct replacement for Rooney, whose elusiveness makes him quite effective in the hole, as Gerard Houllier has already discovered.
Young's contribution enabled England to complete their first win in Scandinavia in nine attempts since 1992, just after Wilshere and Eriksen were born.
Wales do not offer the same threat but the same result in Cardiff on March 26 will do nicely when the challenge to reach Euro 2012 begins again.