Simpson netted from a seemingly impossible angle six minutes after the interval to condemn Wolves to a fifth match without a win.
Hull took the lead in the match with 29 minutes gone.
Liam Rosenior was upended by Tongo Doumbia and Sone Aluko stepped up to curl a 20-yard free-kick around a poorly positioned wall and into the bottom corner.
Wolves could have been level before the interval when Kevin Doyle squared across goal for Dave Edwards, but Ben Amos was out quickly and bravely to block his toe-poked effort.
In the 51st minute, Simpson showed first endeavour and then ingenuity, racing onto a Robert Koren ball that looked to be going out of play before steering a powerful shot across goal and in off the far post for his sixth of the campaign.
The stunned visitors were almost handed a route back into the match when Bakary Sako escaped down the left and whipped in a cross that deflected off Paul McShane's heels but fell kindly for Amos to gather.
McShane was less fortunate in the 67th minute when he clumsily allowed a weak cross through his legs and in the subsequent scramble Chester diverted into his own net.
That signalled an uncomfortable last quarter of the game for Hull, with Sako's deflected free-kick flying over the bar and Doyle narrowly failing to connect with Stephen Ward's cross.
Simpson dragged wide from 18 yards in injury time when he should have made it 3-1, but victory means the Tigers are still within striking distance of the leaders.