Preston, on the other hand, who played one game less over the festive season, showed why their unbeaten run has now extended to 16 games.
Referee Miller did not help the Norwich cause when he failed to give two possible first-half penalties, while his decision to penalise Darren Huckerby in first-half stoppage-time contributed to the visitors' opening goal.
Things went from bad to worse after the break. Craig Fleming was adjudged to have handled and Graham Alexander made it 2-0 from the penalty spot, before David Nugent added a third when he robbed Simon Charlton and smashed the ball past the advancing City keeper.
The home side looked far from their best for the opening 25 minutes.
Paul McVeigh then brought a smart save from Carlo Nash with a well struck shot from an acute angle.
At the other end, Adam Nowland's long-range effort was an easy catch for Robert Green.
Seven minutes before half-time McVeigh released Huckerby, but his first touch was too heavy and Nash was able to gather the ball with some ease.
Nash then flattened Huckerby on the edge of the penalty area as he punched the ball away, but the referee gave a corner, as the outraged home fans demanded a penalty.
The visitors took the lead on the stroke of half-time when Alexander's throughball was toe poked inside Greens left hand post by Nowland.
The hosts should have equalised two minutes into the second half when Jim Brennan, on for the injured Carl Robinson, shot at Nash when put through by Dean Ashton.
Craig Fleming forced Nash into a fingertip save with a long-range shot before Mr Miller further annoyed the home fans by awarding a penalty against Fleming, when the ball appeared to hit his hand.
Alexander's low right-foot spot-kick beat Green's despairing dive to his right.
Nugent then rubbed salt into the wound when he dispossessed Charlton and raced on to crash a fierce right-foot shot inside Green's left hand post from nine yards.