Jan Vennegoor of Hesselink opened the scoring on 11 minutes but Wolves were level just after the break thanks to a freak own goal by Anthony Gardner.
A Stephen Hunt penalty helped City restore their lead minutes later but Matt Jarvis made sure of a point for the visitors with a deflected 67th-minute strike.
City took the lead on 11 minutes when Jozy Altidore managed to hold off his man before slipping a neat throughball to Vennegoor of Hesselink who had the space to hit a superb left-footed shot into the bottom corner of the net to register his third goal of the campaign.
Wolves came close to equalising moments later when Jarvis' corner found the head of a towering Kevin Foley but the defender's close-range effort flashed just past the post.
Stephen Ward then tried his luck for the visitors but his thunderous left-footed strike from 25 yards flew just wide of keeper Boaz Myhill's right-hand post.
Mick McCarthy's men were level within minutes of the of the second half as a cross from Ronald Zubar was met with a calamitous attempt at a clearance by Hull defender Gardner, whose right-footed slice sent the ball looping over Myhill and into the back of his own net.
City were soon back in front however as referee Mike Dean awarded the Tigers a penalty after Zubar was adjudged to have pushed Altidore inside the box.
Hunt took the resulting spot-kick and made no mistake with an arrowed left-footed strike into the top corner to make it 2-1.
David Jones went close for Wolves just after the hour mark but his low left-footed shot was turned away by Myhill.
Altidore then created a chance for himself moments later when the Villarreal loanee raced past the Wolves defence and hit a low right-footed shot but keeper Marcus Hahnemann was equal to it with a smart save down to his right.
Wolves were level again on 67 minutes when the Hull defence failed to clear a cross from Foley which found its way to Jarvis at the back post. His deflected right-footed shot curled into the back of the net from 12 yards.
Substitute Geoffrey Mujangi had the chance to steal all three points for Wolves in stoppage time when City again failed to clear their lines but the Belgium international's right-footed shot was saved by Myhill.