Pilkington, a former United trainee, stole a yard on Chris Smalling before looping a header over Anders Lindegaard on the hour mark.
Sir Alex Ferguson brought on Paul Scholes and Danny Welbeck in an attempt to once again turn around a deficit but there was no way back for United and they have now surrendered top spot in the Premier League to rivals Manchester City.
The Red Devils had settled quickly into their passing game early on and Robin van Persie forced a save from John Ruddy in the Norwich goal within minutes.
The England international goalkeeper also got down well to prevent Ashley Young finding the breakthrough later in the half as Michael Carrick and Ryan Giggs looked for an opening.
But Norwich were an intermittent threat at the other end with Wes Hoolahan finding space between the lines and Smalling was forced into a smart interception to deny Grant Holt.
The pattern continued after the interval as the game remained open but with neither side able to find a clear opening.
However, it was no surprise that the impressive Hoolahan was the architect when the goal finally came.
The Republic of Ireland international spread the play wide for Javier Garrido to cross and Pilkington was there to head over the helpless Lindegaard.
The lead was no more than the Canaries deserved from a spirited display and, while United continued to probe away in search of an equaliser, they found Ruddy in wonderful form.
He managed one final superb save from substitute Anderson deep into injury time and Chris Hughton’s side held on for the three points.