In a tight first half in Saturday's League One clash at Hillsborough, Brian Wilson fired over for the U's from 20 yards before Wednesday thought they had taken the lead on the half hour mark.
Gary Madine turned home Ben Marshall's long throw only for the goal to be ruled out for an adjudged foul on Andy Bond by Chris O'Grady.
Madine headed onto the bar after the restart before Wednesday opened the scoring in the 59th minute through captain Jones.
U's keeper Ben Williams could only palm Madine's stinging left-footed effort and the giant defender was on hand to slide in the rebound.
O'Grady was then denied by Williams before the Owls doubled their advantage with 20 minutes left. Chris Lines' searching free-kick was misjudged by Madine but defender Johnson was alert to bundle home from close range.