Two second-half free-kicks from Akos Buzsaky gave Plymouth their first win at Norwich in 46 years.
Youssef Safri handed Norwich the lead on the stroke of half-time with a 25-yard free-kick.
But Plymouth equalised when Barry Hayles headed his ninth goal of the season from Hasney Aljofree's corner.
Hungarian Buzsaky then put Argyle ahead when he found the top left-hand corner from 20 yards, before crashing in his second off the underside of the bar.
# Norwich manager Peter Grant:
"We were poor. In the second half it went from worse to worse.
"To concede two goals from free-kicks beggars belief. Too many players were mentally weak, content to pass the buck to someone else. It was unacceptable.
"We do not give ourselves a chance when we play like that. Too many players are in the comfort zone. The group will be changed, make no mistake about that."
# Plymouth boss Ian Holloway:
"I had a couple of new people in and it looked as though we were strangers at times in the first half.
"I just told the lads to play the football that I know they are capable of and I was delighted with our second half performance.
"There's no doubt we have a lot of talent here and they certainly showed that after the break. Now the challenge is to build on this."
Norwich: Gallacher, Colin (Robinson 86), Doherty, Shackell, Drury, Croft, Safri, Etuhu, Huckerby, Dublin, McVeigh (Brown 65).
Subs Not Used: Lewis, Hughes, Martin.
Booked: Safri, Doherty.
Goals: Safri 45.
Plymouth: McCormick, Gosling (Hodges 70), Sawyer, Seip, Aljofree, Norris, Buzsaky, Nalis, Halmosi (Summerfield 83), Hayles (Reid 88), Gallen.
Subs Not Used: Clapham, Laird.
Booked: Buzsaky, Norris.
Goals: Hayles 59, Buzsaky 63, 75.
Att: 23,513
Ref: M Jones (Cheshire).
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