Akpo Sodje's first goal for Wednesday drew the Owls level after Sylvan Ebanks-Blake's penalty a few minutes earlier, and Burton O'Brien soon added the winner.
It was the first time the Pilgrims had been beaten at Home Park since mid-March and saw them drop a place in the Championship table.
Argyle led within 90 seconds of the start of the second half, when Ebanks-Blake netted his sixth Championship goal of the season from the penalty spot after Frankie Simek had fouled Peter Halmosi.
Pilgrims boss Ian Holloway included new signing from Wycombe Jermaine Easter on the substitute's bench in the only change to the squad which had seen a five-match unbeaten run come to an end at Preston seven days earlier.
Referee Andy D'Urso had no hesitation in pointing to the penalty spot after Wednesday's American defender Simek tripped Halmosi to end Argyle's first attack of the second half.
Ebanks-Blake's powerful low shot left Wednesday goalkeeper Lee Grant with no chance.
But Wednesday were behind for less than five minutes before Sodje converted a shot in from a near impossible angle, taking Simek's throw-in on his chest and tuning to hook the ball in.
Then Sodje turned provider as right-winger O'Brien scorched through the Argyle back four onto his pass.
The Scot held off Marcel Seip's challenge to fire a shot low past Pilgrims goalkeeper Luke McCormick, who had been slow to come off his line.
Easter and fellow substitute Rory Fallon came on just after Ebanks-Blake's spectacular shot was blocked by Michael Johnson.
Between them they had three reasonable headed chances to find the elusive equaliser, but Wednesday hung on for three deserved points.