The forward's miss-hit volley from Joe Mattock's corner after 12 minutes some how went in to reward the hosts for their early pressure.
The Owls almost took the lead after two minutes but Gary Madine headed Antonio's inviting cross inches wide.
Jermaine Johnson, operating just behind Madine, then charged forward and let fly from long range and goalkeeper Scott Gallacher did well to hang on to his fierce shot.
Rangers had offered little as an attacking force but against the run of play they threatened three times in the space of five second-half minutes.
Nicky Law, formerly of Sheffield United and Rotherham, dragged a shot wide from an acute angle. The diminutive midfielder then played in Andrew Little, who stung the palms of the goalkeeper. Shortly after the hour mark, Little then flashed a shot narrowly wide.
But back came Wednesday and Madine, on the stretch, stabbed Chris Maguire's teasing cross over the top.