The Canaries won the battle between the newly promoted sides thanks to brace from ex-Huddersfield man to continue fine start to the season as Swans drop into bottom half
The match was the first meeting between any of the Premier League's newly promoted sides and Norwich backed up its standing as the highest placed of the three with a fine performance.
Leon Britton returned to the Swans' line-up after recovering from injury during the international break, with Steve Morison keeping his place ahead of Grant Holt for the hosts.
Norwich's Carrow Road was bathed in sunshine and the Canaries made the brightest possible start. Elliot Bennett's cross was headed back into the area by Morison and Pilkington was on hand to smash the ball in to give Norwich the lead inside the first minute.
Paul Lambert's men had started the game at a ferocious pace and could have had a chance to double their lead just minutes later as Morison looked to run through one-on-one before being hauled down by Swansea skipper, Monk who was booked.
Norwich did double their lead in the tenth minute, however after Martin was given a free header from David Fox's free-kick.
Just as it looked to be a tough afternoon developing for Brendan Rodgers, his side grabbed an instant goal.
Scott Sinclair burst down the left hand side leaving Naughton and Bennett in his wake, slipped in the area and managed to prod the ball into the path of Graham, who swept in his second goal in as many games.
The game continued at break-neck speed, with both sides creating dangerous opportunities that Graham and Morison failed to finish off. Swansea looked to test Norwich goalkeeper John Ruddy from distance as it came into the ascendancy, but couldn't conjure up anything particularly dangerous.
Norwich had some chances of its own, and although Swansea continued to enjoy the better of possession before the it half, it was nearly made to pay for its profligacy in front of goal when Michel Vorm was caught out and found himself lucky to see Bennett's cross drift over his bar.
The Canaries started the second half in a similar vein to the first, with Morison looking particularly dangerous. However, another player would get the third goal for the Canaries – a Norwich corner fell to Johnson who was unable to shoot but prodded the ball to Pilkington, who swivelled and put in his second of the game to restore Norwich's two-goal cushion.
Morison was forced off through injury shortly afterwards and was replaced by Norwich club captain, Grant Holt.
Scott Sinclair tried to take the game to Norwich, hitting another long-range effort but failing to hit the target as Brendan Rodgers continued to tweak his lineup to try and find a way to make his team's improved play count.
The game's substitutions had slowed the tempo slightly which was playing into the hands of Swansea's possession game and they had a chance to grab a goal following Danny Graham's surging right-wing run but Dobbie's shot was blocked and his follow-up header drifted comfortably into Ruddy's arms.
As the game entered the final ten minutes, Norwich began to sit back and allow Swansea more and more of the ball. Brendan Rodgers' side was unable to create a chance though and has now lost its first four Premier League games of the season, mirroring its early away form to last season in the Championship.