Barry Hayles put the Pilgrims level with a close-range header and two free-kicks clinically put away by Akos Buzsaky gave Argyle their second 3-1 victory over the Canaries this season.
The result sees Norwich slip towards the wrong end of the table, giving manager Peter Grant a real headache now that his top striker, Robert Earnshaw, is sidelined with a groin injury.
Argyle kicked off attacking the River End goal. The Norwich game plan involved getting the ball to Darren Huckerby at every opportunity, so that he could put pressure on young right-back, Dan Gosling.
This tactic saw the home side create several chances in the first 20 minutes without finishing any of them.
After 24 minutes, Dion Dublin got his head to Youssef Safri's right-wing free-kick, but the ball sailed harmlessly over the bar.
Safri was booked after 29 minutes for a fairly innocuous challenge.
Three minutes later Dickson Etuhu got up well to meet Lee Croft's right-wing cross, but headed wide.
Gary Sawyer rescued the visitors when he blocked Etuhu's close-range shot from Paul McVeigh's low cross from the left and Buzsaky was booked for pulling back Huckerby five minutes before the break.
Gosling then threw himself in front of Huckerby as the City winger burst into the Argyle penalty area, but referee Michael Jones gave a free-kick to Plymouth.
Pilgrims defender Marcel Seip fouled Dublin 25 yards from goal and Safri's right-foot free-kick beat McCormick low to his right.
The visitors started the second half in determined fashion and hit the woodwork with Buzsaky's inswinging left-wing corner.
At the other end, Croft's shot was turned for a corner by McCormick and then his right-wing cross was blocked as Dublin looked certain to score.
Huckerby raced on to Etuhu's through ball but fired over when a cross might have been more productive.
The miss proved costly as Hayles headed the equaliser when Hasney Aljofree turned Peter Halmosi's right-wing corner back across goal.
Gary Doherty was booked for fouling Buzsaky, who picked himself up and beat Paul Gallacher to his right with a curling right-foot shot from 22 yards to put the visitors 2-1 in front just past the hour.
Buzsaky wrapped up the points for Plymouth 15 minutes from time with another right-foot free-kick which hit the bar and crossed the line before bouncing back into play.
Debutant Chris Brown tried his luck with an overhead kick after coming on as a substitute for McVeigh, but the ball went straight into the keeper's hands as Plymouth held out for a well-earned victory.