The first Canaries goal came when Paul McVeigh carried the ball into the Plymouth penalty area from the halfway line and unleashed a shot that Romain Larrieu could only palm onto the boot of Mathias Doumbe, who turned it into the net while trying to clear.
Dean Ashton settled the home fans' nerves when he scored the second eight minutes from half-time.
This proved to be enough against an Argyle side who were later criticised by caretaker boss Jocky Scott for their failure in front of goal and basic errors in defence.
The home side started well and after ten minutes Ashton appeared to be pushed out of his stride as he burst towards the Plymouth goal, but referee Barry Knight waved play on.
Norwich then forced three corners with Ashton heading over when he got to the third, well delivered by Jim Brennan.
Paul Wotton's shot shaved a post before the Canaries went ahead in the 20th minute when McVeigh's shot was saved by the goalkeeper but turned into the net by the luckless Doumbe.
The lead was doubled after 37 minutes when a patient build-up enabled Jurgen Colin to deliver a right-wing cross, and Ashton volleyed home from six yards beyond Larrieu's despairing dive.
Three minutes before the break the Plymouth keeper did well to keep out Ashton's low left-foot drive.
The first half ended with Mr Knight awarding an indirect free-kick in the City penalty area after Youssef Safri's boot came into contact with David Norris' head. It was followed by a confrontation that earned yellow cards for Colin and Mickey Evans.
Ten minutes into the second half Ashton thundered a right-foot shot against the post, while, at the other end, Robert Green had to save shots from Bojan Djordjic and Anthony Barness.
Twenty minutes from time Ashton's angled drive was just inches away from the target.
New loan signing Kevin Lisbie, the Charlton forward, came off the bench with 17 minutes to play and almost made an immediate impact, heading home only to see the offside flag rule his effort out.
However, the home fans were more than happy to celebrate their first Championship victory of the season.