The Pilgrims caused huge problems for Glenn Roeder's men all afternoon and could easily have won by a larger margin against abject defending by the visitors.
The icing on the cake was a first-ever goal for Argyle right-back Paul Connolly, making his 149th start for his only professional club.
Connolly, 24, netted the Pilgrims' crucial second goal less than two minutes after half-time after linking up with right-winger Lee Martin on the flank and continuing his run into the box.
Martin, on loan to Argyle from Manchester United, had opened the scoring midway through the first half with an impudent overhead kick, after Norwich's poor defenders had failed to clear Connolly's long throw-in.
It did not take Argyle too long after their second goal to set the seal on a fine win, with Sylvan Ebanks-Blake setting up midfielder David Norris for a first-time volley that gave Norwich goalkeeper David Marshall no chance.
It should have been four immediately afterwards as the Pilgrims continued to rip Norwich's back-line apart, but Ebanks-Blake blasted over from three yards after being played in by Barry Hayles.
After that, Argyle stepped off the gas and Norwich had a few bright moments to lighten their gloom. Late on, both Darel Russell and Jamie Cureton hit the post.
However, any consolation would have been scarcely deserved as the Pilgrims dominated the entire proceedings, giving Roeder a clear indication of the hard work that lies ahead of the new City boss.
It is his defence which should give him most concern, a situation not helped by an injury to on-loan Birmingham centre-back Martin Taylor which saw him subbed off before half-time.