Norwich have only conceded seven goals in the league this season and having led 1-0 at half-time they played well enough in the second half to deserve their three points.
Preston's Jamaican striker Ricardo Fuller had a two yard right foot shot from on the left hand side of the six-yard box saved by Norwich City goalkeeper Richard Green after 20 minutes.
Three minutes later Paul McKenna hit over an outswinging right footed corner and Preston captain Chris Lucketti rose to send a header narrowly high and wide of the left hand post.
In the 33rd minute Fuller was booked by referee Mr Rejer after sliding in on Paul McVeigh, Norwich City's leading goalscorer.
Only a minute later Norwich took a 1-0 lead through Davd Nielsen. McVeigh won the ball in midfield and found Phil Mulryne who in turn found Nielsen, who beat Lucketti and put the ball past the Preston keeper and into the bottom left hand corner of the net.
This was Norwich's only on-target effort of the first half.
Preston came out strongly in the second half and Richard Cresswell scored his fifth goal of the season to equalise in the 51st minute.
Eric Skora had flicked the ball on under pressure and Cresswell curled a shot from 15 yards into the bottom right hand corner of the net.
Norwich made it 2-1 after 54 minutes when McVeigh hit a five-yard overhead kick from the left hand side into the bottom right hand corner.