The home team came close to taking the lead midway through the first period when the ball fell to Bryan Hughes on the edge of the area, but his clever curling effort floated just wide of the left-hand post.
Hull were awarded a free-kick on the edge of the Owls box in the 33rd minute after Tommy Spurr had brought Caleb Folan down with a mistimed tackle. Veteran striker Windass stepped up to curl a wonderful 25-yard right-footed effort into the top corner of the net to give Phil Brown's men the lead.
The visitors came within a whisker of equalising just after the break when Akpo Sodje burst into the box at speed and fired in a right-footed shot which rebounded back off the inside of the post, and Hull were able to clear the danger.
Michael Turner pushed forward midway through the second half and came close to doubling the Tigers' lead. Wayne Brown floated a ball into the box towards his fellow centre-back, but Turner could only head the ball straight into the arms of keeper Lee Grant.
Wednesday had a chance to grab a point in the dying moments of the game when Glenn Whelan played in a clever free-kick which found substitute Francis Jeffers in the box. However, the ex-Arsenal and Everton striker could not beat keeper Boaz Myhill as his right-footed effort was well-saved by the Hull number one.