The one-goal margin was a travesty for the Canaries, who led from the 13th minute, hit the woodwork three times, and had a goal disallowed.
Argyle, without a win all season, were a well-beaten side even before centre-back Krisztian Timar was sent off ten minutes before the break for a second yellow card.
By that time, the Canaries led thanks to Arturo Lupoli's strike, and secured the three points when new loan signing Antoine Sibierski drilled home a long-range free-kick early in the second half.
Even a late consolation goal for the Pilgrims from home debutant Paul Gallagher could not put any gloss on the home side's performance.
Norwich took the lead when, after being put through by Sibierski, Lupoli responded to a ricochet off Argyle's Dutch defender Marcel Seip to shoot past goalkeeper Graham Stack and into the top corner.
Matty Pattison saw a 25-yard drive smack off the underside of the bar with Stack well beaten and, although Lupoli tucked home the rebound, it was ruled offside.
Pattison shot over from six yards in front of an open goal before Timar was dismissed for a second petulant foul on Sibierski.
Lupoli saw an early second-half header cannon off the crossbar before Gallagher conceded a free-kick for handball around 30 yards out and Mark Fotheringham teed up Sibierski for a low drive into Stack's bottom left-hand corner.
Stack saved well from Darel Russell, and Pattison hit the bar again, as the visitors tried to force home their advantage before Argyle sent on Belgium international Emile Mpenza for his debut.
The former Manchester City man nearly scored when Canaries keeper David Marshall flapped at a high ball, but Mpenza saw his first-time shot cleared off the line by Ryan Bertrand.
Deep into stoppage time, Argyle substitute Rory Fallon knocked the ball down to Gallagher, who lashed a shot past Marshall. However, it was too little, too late.