Miguel Angel Llera then thought his header had crossed the line but it wasn't given as Wednesday continued to push for an opener.
Hull's best opening of the first 45 came when Paul McKenna volleyed on the edge of the area but it flew just wide.
Wednesday then thought they had earned a spot kick soon after the interval when Michail Antonio seemed to be brought down but it wasn't given.
Hull had had the better of the second half and got their goal 13 minutes from time when Aaron McLean beat Chris Kirkland from inside the area.
Hull remain 10th despite the win, while Wednesday drop into the bottom three.