On 20 minutes, against the run of play, Simon Whaley put in a low cross from the right which caused problems for Gary Doherty who managed to scramble the ball away for North End's first corner of the game.
At the other end, Darren Huckerby, Robert Earnshaw and Lee Croft had shots blocked by defenders.
After 28 minutes Paul Gallacher had to be alert saving shots from Whaley and Danny Pugh.
Ten minutes from the break Croft's right-wing cross was tipped away by Nash and fell at the feet of Huckerby, but his snap-shot went inches wide of the post.
A minute later Matt Hill was booked for a foul on Croft.
Three minutes from half-time, Nash did exceptionally well to block Carl Robinson's shot after he had dribbled through the Preston defence to the corner of the six-yard box.
City old boy Jason Jarrett was booked in stoppage time for fouling the City new boy Croft.
Ten minutes into the second half Huckerby's diagonal cross-cum-shot from the left found the net off Sean St. Ledger's right boot as the former Peterborough defender attempted to clear.
As the home side threatened to run riot, Brian Stock made way for Chris Sedgwick after 65 minutes.
After 69 minutes Croft made way for Paul McVeigh and five minutes later Nash saved from McVeigh and Gallacher saved from Nugent.
A minute later Huckerby's left-ring cross was just too deep for Earnshaw to get his volley on target at the far post.
Pugh then made way for Patrick Agyemang before Norwich went two goals up after 82 minutes.
McVeigh crossed from the right and Earnshaw beat Nash at the far post with a crisp right-foot volley from 12 yards.
In stoppage time Preston's skipper Graham Alexander was sent off for a crude challenge on the Norwich captain Adam Drury.
To rub salt into the Preston wounds former player Dickson Etuhu was named man-of-the-match.