He had the lion's share of the Bantams chances, but in the end it was a piece of individual brilliance from Darren Holloway that was the difference between the two sides.
Holloway's superb 25-yard shot after 77 minutes was one of the only bright spots in what was largely a quiet and incident-free local derby.
Bradford started the brighter, with Windass shooting wide in the third minute, sparking derision from the massive Tigers crowd.
He headed over in the seventh minute and in the 15th minute Holloway headed wide in what was his, and Bradford's, best chance of the game so far.
Worryingly for the Tigers, they did not seem to be dealing convincingly with the increasing threat Windass posed.
After 19 minutes, a looping header from Junior Lewis went just over after Stuart Elliott had done well to win the ball and put in a dangerous cross.
Hull were beginning to pick up the pace as the half went on, and Aaron Wilbraham put a header wide in the 23rd minute.
Windass missed the target two more times, before Elliott shot wide in first-half stoppage time.
In the second half, Windass nearly exploited some sloppy defending by the Tigers but Hull again raised the tempo with two quick corners in succession, and their dominance was all the more evident with the 12 corners they eventually won. However, neither team were putting the keepers under threat.
In the 70th minute, Ben Muirhead raced into the area and shot inches over from ten yards when he could, and should, have done much better.
But seven minutes later it was Holloway who took all three points for Bradford when he unleashed a rasping shot that gave Boaz Myhill no chance.