Canaries goalkeeper Paul Gallacher had already denied David Nugent with a low save when Pergl pounced with a dipping drive from 30 yards after 26 minutes.
Daniele Dichio doubled the advantage from close range when he was teed up by Paul McKenna and Seyfo Soley and Simon Whaley went close to making it three.
City roused themselves when Lee Croft hit the upright before Jason Shackell headed in, but Preston held on to win.
Preston manager Paul Simpson:
"I thought Pavel Pergl did very well.
"I think the pace of the game will take a bit of getting used to for him, but he gives us a good option in shoring up the midfield allowing Paul McKenna, Danny Pugh and Simon Whaley a bit more freedom to get forward.
"Every single day in training he comes and does his finishing and he's probably one of the last ones to come off.
"I've seen how he can strike a ball and that wasn't one of the cleanest he's ever hit, but if you get it on target you just never know what might happen."
"I think it was plain for everybody to see - we lost two bad goals, but we dominated from start to finish.
"That's the last three league games now where we have battered everybody, but we've got minimal points.
"There was a lot of good football there, a lot of good knowledge and a lot of good understanding, and to come away from Preston, where we have battered them, with a defeat is very disappointing.
"I know football is all about winning games and that's what I'm judged on but if we play like that I'll be more than happy. I've played here with so-called better teams and never dominated a game as much as that."
Preston: Lonergan, Wilson, Soley (St. Ledger 82), Chilvers, Hill, Whaley, Pergl, McKenna, Pugh, Dichio (Agyemang 79), Nugent (Mellor 85).
Subs Not Used: Henderson, Sedgwick.
Goals: Pergl 28, Dichio 43.
Norwich: Gallacher, Doherty, Shackell, Dublin (Thorne 24), Drury, Croft, Hughes, Fotheringham, Lappin, Brown, Martin, Thorne (McVeigh 46).
Subs Not Used: Lewis, Eagle, Colin.
Booked: Fotheringham.
Goals: Shackell 62.
Att: 11,601
Ref: P Dowd (Staffordshire).