Owls midfielder Paul Corry, who had been making Wednesday tick in recent weeks, suffered an injury and had to be replaced by fit-again Rhys McCabe and that disrupted the hosts' flow.
With Peterborough unable to take advantage the game descended into a low-quality affair played mainly in the middle third, with the half-time whistle coming as a relief to all.
However, the game needed less than 20 seconds after the restart to come to life and it was the hosts that forged into the lead.
Virtually straight from kick-off the ball was pumped up to Chris O'Grady, he flicked on and Ross Barkley fired home from inside the penalty with an effort that appeared to be deflected.
Wednesday thought they had made the game safe with 14 minutes to go when Miguel Llera headed home Michail Antonio's cross from six yards out for his third goal of the campaign to double their lead.
But Posh finally stirred and immediately gave themselves a lifeline when George Boyd drilled in from the edge of the area following a corner.
However, Darren Ferguson's men were unable to launch a late onslaught and Wednesday saw it out relatively trouble-free.