The result sees Darren Ferguson's men keep alive their hopes of beating the drop, while also ensuring that the Owls still have work to do.
The Owls threatened once more when Posh failed to deal with a corner, presenting Seyi Olifinjana a chance to volley at goal.
However, brave defending saw three players throw their bodies in the way before the ball was hacked clear.
The score remained goalless at half time but the deadlock was broken in the 64th minute by Grant McCann, who found the top left corner from 25 yards out with a superb left-footed strike.
Wednesday put plenty of pressure on their opponents, with Leroy Lita firing over with late on, but the hosts held firm to bag three valuable points in the scrap for survival.