The former Old Trafford youth player scored the only goal of the game with a sublime header as Sir Alex Ferguson's side relinquished top spot in the Premier League to rivals City
Pilkington, a former Old Trafford youth player, headed the Canaries in front from an excellent Javier Garrido cross.
John Ruddy was forced into a stoppage-time save off the head of Sebastien Bassong and second-half substitute Danny Welbeck went close with a deflected header, but Chris Hughton's side held on for a famous three points.
Sir Alex Ferguson was without Wayne Rooney due to tonsillitis, and David De Gea who required dental work on his wisdom teeth.
But the visitors launched straight into the ascendancy and went close in the third minute through Robin van Persie, who forced Ruddy into a save with a low, curling effort.
Norwich responded immediately as Robert Snodgrass blasted over with a speculative volley, before Pilkington dragged a shot across goal after a clever Wes Hoolahan pass.
The two sides traded chances early on as Ruddy was tested again by an Ashley Young free kick in the 15th minute but saved comfortably, and Hoolahan found space 20 yards from goal but could not beat Anders Lindegaard.
The hosts should have gone ahead after 25 minutes, when Pilkington’s clever disguised pass released Garrido on the left-hand side, but Grant Holt could not connect with the full-back’s driven cross-shot.
Norwich impressed in the first half and continued to create chances as Snodgrass wrong-footed Rio Ferdinand after more good work from Hoolahan and only a last-ditch interception from Chris Smalling prevented Holt from shooting.
Sir Alex Ferguson’s side finished the half the stronger as Van Persie tried the spectacular but failed to connect with a long ball from Ryan Giggs, and Ruddy was called into action by Young again, pushing a powerful attempt around the post.
The visitors started brightly after the interval and went close through the Dutchman, who brought down a pass from Young and held off a challenge, only to scuff a shot harmlessly into Ruddy’s body.
But Norwich were ahead just before the hour mark, when a superb move involving Hoolahan and Holt released the overlapping Garrido, whose cross from the left wing was brilliantly headed over and beyond Lindegaard by Pilkington, who had timed his run perfectly.
Trailing with just over 20 minutes to play, Sir Alex Ferguson made two changes as Paul Scholes came on for Antonio Valencia and Danny Welbeck replaced the anonymous Chicharito.
The substitutions had an immediate effect as Scholes began to control the midfield and Welbeck nearly pulled his side level, but his header from a Young cross deflected off Bassong and wide for a corner.
Norwich responded, bringing on Steve Morison and Johnny Howson for Holt and the influential Hoolahan, while Anderson came on for Rio Ferdinand in a final throw of the dice for the Old Trafford club.
The hosts had the chance to kill the game off on the counterattack as Morison played in Howson, but with just Lindegaard to beat the midfielder dragged his shot hopelessly wide.
Ruddy was twice called into action late on, first tipping over a Bassong header, before managing to hold on to a stinging Anderson drive to ensure the Canaries took all three points.