Steve MacLean's winner ended Sheffield Wednesday's unbeaten home record.
Leon Clarke fired narrowly wide for the Owls early on before MacLean scored against the run of play with a neat turn and finish from six yards out.
Clarke missed a chance to level when he shinned his shot when one-on-one with Plymouth keeper Roman Larrieu.
Wednesday continued to dominate but Argyle held out after Akpo Sodje headed wide for the Owls and Jermaine Johnson shot wide with the goal gaping.
Sheffield Wednesday boss Brian Laws:
"We had about 90% of the ball, but we didn't have the guile. That's what disappointed me.
"I had two wingers and I don't think they performed anywhere near what they can. Our strikers fed off scraps.
"It's our first defeat (at home) and it's hard to take. No disrespect to Plymouth but we're better than that."
Plymouth boss Paul Sturrock:
"Steve MacLean came to the show and showed me all the things he should do and he reaped the benefits with a goal.
"I thought his performance was what I signed him for.
"We got the lead and decided that's it. The players decided it was trench warfare and to be fair they've managed to get the win."
Plymouth: Larrieu, Cathcart, McNamee (Walton 62), Barker, Seip, Duguid, Paterson (Timar 74), Clark, Summerfield, MacLean (Fallon 68), Gallagher.
Subs Not Used: Noone, Marin.
Booked: McNamee, Gallagher.
Goals: MacLean 23.
Att: 16,515
Ref: Graham Laws (Tyne & Wear). Make your Championship predictions
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