The Owls won it thanks to a goalkeeping howler from the Tigers' Eldin Jakupovic, who inexplicably dropped Miguel Llera's corner over the line and then had to leave the field wearing a neck brace after Reda Johnson had clattered into him.
Hull wanted a foul for Johnson's challenge, which led to a 10-minute stoppage, but Haywood waved away appeals and Wednesday made sure of the points in the seventh minute of injury time when Michail Antonio raced clear and rolled home.
Wednesday's second goal had come just four minutes after Hull had drawn level thanks to Robert Koren's header, which cancelled out Johnson's first-half opener for Wednesday.
That was not Haywood's only involvement in the game, though, as the West Yorkshire official inexplicably ruled out a Giles Coke effort for an apparent foul on the wobbly Jakupovic.
Whatever the circumstances of Wednesday's win, it was thoroughly deserved as despite only playing winger Antonio in a lone striker's role, they put in a superb display and could have won even more convincingly.
For Hull, it was a first loss since November 24 and they are unlikely to have played so poorly before in what has been an outstanding first half to the campaign.
But to translate that into promotion manager Steve Bruce may need to recruit a goalkeeper after Jakupovic's shaky display.