He made no mistake from the spot - sending Wayne Hennessey the wrong way after Neill Collins had brought down Richard Garcia.
It was a case of job done for Windass, whose strike earned Hull a success that was inspired by new signing Jay-Jay Okocha.
The former Bolton talisman ran Wolves ragged for spells and showed what a threat he will be at Championship level.
Despite the influence of Okocha, Wolves really only had themselves to blame for their third defeat in four games - and their second in succession in front of their own fans.
They would have been well in control of affairs by half-time had the finishing of Andy Keogh and Stephen Ward been better.
Their frustration in front of goal was summed up 18 minutes from time when three-goal leading scorer Freddy Eastwood finally found an opening only to see his 20-yard drive crash off the bar.
While Okocha caught the eye for Hull and set-up an early chance for Bryan Hughes that was saved by Hennessey, Wolves created the best opportunities in the first half.
But Keogh was badly at fault with the two that came his way. He headed straight at goalkeeper Boaz Myhill from close range in the 15th minute after being picked out by a cross from Michael Kightly. The Republic of Ireland international then blazed over the bar in the 37th minute when he only had Myhill to beat.
In between those misses, Ward had seen his header cleared off the line by Michael Turner after more good work by Kightly.
While Wolves may have had the best chances, Hull had the stand out performer in Okocha.
He was a constant menace to the Wolves defence and at one stage it took five defenders to stop another surging run from the former Nigeria star.