The City defence refused to be overawed even when Sir Alex Ferguson introduced rested stars from the bench.
Cristiano Ronaldo, Wayne Rooney and Ruud van Nistelrooy all showed some classy skills, but failed to find a way past Robert Green and the men in front of him.
The visitors kicked off attacking the River End goal.
Green was called into action but it was only to gather a scuffed shot from Kleberson after good work on the right by Gary Neville.
Norwich had a short spell of attacking in which keeper Tim Howard was put under pressure by a rather risky backpass. After that the Canaries found it hard to get the ball away from United without being threatened by the away side.
Leon McKenzie did well in his own penalty area to head away Kleberson's free-kick, while at the other end he whipped in a cross from the left wing which was intercepted before it reached the well placed Damien Francis.
In the 22nd minute Ronaldo replaced the injured Louis Saha and was soon in the thick of the action, fouling Darren Huckerby who had beaten him for pace on the City left.
Ronaldo then put over a good cross from the right wing but neither Alan Smith nor Kleberson had anticipated that it would reach them.
After half an hour another Ronaldo cross produced the first corner of the game, but once again the energetic McKenzie was on hand to head away the flag-kick.
It was then Norwich forcing three corners without making any of them count.
Ronaldo moved into a central role but fired wide when the ball came to him. He then repeated the shot after cutting in from the right wing and the half ended with honours even.
Both managers made a half-time change, David Bentley making a first appearance after a long lay-off through injury to replace Graham Stuart, while Rooney came on for Quinton Fortune.
Bentley put in a cross from the right, but Ashton was unable to test Howard with his header.
Rooney tried his luck with a long-range shot but it drifted wide of the target.
Good work by Huckerby and Adam Drury released McKenzie but his angled shot was well saved by Howard.
Rooney was booked for a foul on Thomas Helveg and when Bentley's free-kick came in from the right Ashton outjumped the visitors' defence to plant a firm header inside the far post.
Ronaldo fired wide from the edge of the area before McKenzie put Norwich two up when his left-foot volley gave Howard no chance. The chance was created as Huckerby fed Ashton, who unselfishly passed the ball to his strike partner 12 yards from goal.
Paul Scholes followed Wayne Rooney into the ref's notebook for a foul on the industrious Youssef Safri.
Craig Fleming then blocked van Nistelrooy's header and Green saved from Rooney.
Ashton and McKenzie failed to pull the trigger when well placed and Francis had a volley blocked when Huckerby picked him out on the edge of the United penalty area.
The ref failed to penalise Rio Ferdinand for a late tackle on Ashton which left both players needing treatment.
In the closing stages Rooney let fly from 35 yards, but Green tipped the ball over the bar, leaving Norwich and Green celebrating their first clean sheet for 24 games while condemning United to a first league defeat in 21 games.
Man of the Match: Dean Ashton – The Canaries' record signing gave a superb all-round display up front and was rewarded with the crucial opening goal for City before setting up the second.