Windass struck first after just five minutes, squeezing a shot past Murphy at his near post after the Scunthorpe keeper had failed to deal effectively with a speculative long-range effort from central defender Michael Turner.
Windass struck again in the 16th minute with a simple close-range header after a poor clearance by Murphy had gifted possession to the visitors.
Hull might have had a third when young striker Fraizer Campbell rifled in a shot for Murphy to redeem himself with a fine save.
It was a poor start by Scunthorpe, who were without a win in their previous five home games.
They began to claw their way back into the derby with striker Paul Hayes only denied by the outstretched foot of Hull keeper Boaz Myhill.
Hayes had another chance when he broke free into the box but could not find the right control, allowing Boaz Myhill a more comfortable save.
But Hayes provided on the stroke of half-time as Scunthorpe got themselves back into the game. His flick sent striker Jonathan Forte racing clear of the Hull defence to spear a shot past Myhill into the bottom corner.
Suddenly the home side were back in the picture and they pressed strongly at the start of the second half but got little change out of a Hull defence in which Turner was a commanding figure.
Windass might have made it 3-1 for the Tigers from a corner but he fluffed his chance of a hat-trick by making a hash of his shot at the far post.
Scunthorpe continued to huff and puff but got nowhere until the game entered stoppage time when leading marksman Martin Paterson missed the chance of an equaliser when he fired wide from 15 yards.
Scunthorpe gave a debut in the closing stages to loan signing Tomi Ameobi from Leeds when he came of the substitutes' bench, and he too had half a chance with a shot on the turn that went just wide.
However, Hull held out for all three points as they continued their climb up the table after securing a third successive win.