Both sides struggled to create clear-cut chances in a game short on quality but it was the Owls who clinched maximum points with a 60th minute goal from Djeidi Gassama.
It was fifth win in six fixtures for an improving Wednesday as Ian Foster's Pilgrims pushed hard for an equaliser in the closing stages but without success.
Substitute Mustapha Bundu had a couple of shooting opportunities from inside the Owls; box but could not convert either of them.
Argyle remained in 16th position after their defeat but 23rd-placed Wednesday are now just two points behind them at the bottom of a now very congested league table.
Adam Forshaw replaced Jordan Houghton in central midfield against the Owls as one of three changes to the starting line-up from the home defeat by Ipswich.
Joe Edwards returned to the team at right wing-back instead of Matty Sorinola, and wore the captain's armband as well, and Ashley Phillips took over from Julio Pleguezuelo in defence, alongside former Wednesday loan signing Lewis Gibson and Brendan Galloway.
Houghton, Sorinola and Pleguezuelo were all named as substitutes, with no place in the matchday squad again for Dan Scarr and Callum Wright.
Conor Hazard continued as Argyle's goalkeeper with Michael Cooper on the bench as he returned.
to Hillsborough for the first time since suffering a serious knee injury in the 1-0 League One defeat by the Owls in February 2023.
Morgan Whittaker had the first scoring chance of the contest when he took on Marvin Johnson, who positioned himself so Argyle's top scorer could not cut inside him, and sent a right-foot shot over James Beadle's goal.
Ryan Hardie then almost got on the end of a cross to the near post from left wing-back Mickel Miller, but could not quite get there as Beadle safely gathered the ball instead.
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