They were comfortably leading at half-time but had to hang on to their lead in the second half.
David Nugent had an early chance in the fifth minute when he hit an 18-yard shot at Paul Gallacher, the Norwich keeper, who could only push the ball away and Danny Dichio had a 15-yard right-foot shot saved a minute later.
Simon Lappin found Dion Dublin with a right-wing cross and the veteran striker was off target from six yards out.
Chris Martin had a 30-yard shot saved and Dichio headed over from a Kelvin Wilson right-foot, right-wing cross.
Dublin suffered a calf strain and had to be substituted by Peter Thorne after 24 minutes.
Lee Croft fired wide from 35 yards but Preston took the lead in the 28th minute when Nugent found Pavel Pergl and the former Sparta Prague player fired a 25-yard right-foot shot into the bottom left-hand corner of the net.
Referee Phil Dowd suffered a hamstring and had to be replaced in the 32nd minute by Mr Haywood, the fourth official.
Simon Whaley fired wide and then Dichio made it 2-0 to Preston after 43 minutes with a right-foot shot into the keeper's bottom right-hand corner of the net.
Norwich replaced substitute Thorne with Paul McVeigh at half-time and that paved the way for the visitors to dominate the second half. Nugent had a header saved before Croft hit the keeper's left-hand post with a 10-yard right-foot shot from the middle of the penalty area.
Norwich pulled a goal back after 63 minutes when a left-wing corner by Mark Fotheringham was headed into the roof of the net by Jason Shackell and it looked like Norwich were right back in the game.
Fotheringham had a shot saved and then there was a series of substitutions by Preston with Patrick Agyemang, Sean St Ledger abnd Neil Mellor replacing Dichio, Seyfo Soley and Nugent respectively.
But Preston held out for an important three points.