Michael Mifsud nearly had the visitors in front ten minutes from half-time as he turned and fired in an arrowed right footed shot from 20 yards, but Hull keeper Boaz Myhill managed to dive full-stretch to parry the ball away.
Hull's Frazier Campbell found himself through on goal minutes from the break but defender Isaac Osbourne brought down the Manchester United loanee. It looked as if Osbourne may have been the last man, but he was only given a booking by the referee despite protests from the Hull fans.
Danny Fox tried his luck from distance for Coventry midway through the second half, but his ambitious left footed effort from 35 yards was comfortably tipped over the bar by Myhill
The home side thought they'd taken the lead on 71 minutes as the ball fell to Campbell in the six-yard box and the striker slotted it neatly into the back of net. However, to the Tigers' dismay, the effort was disallowed as the assistant-referee ruled the young striker to be offside.
But Hull were not to be denied as substitute Folan raced on to a long ball upfield from Wayne Brown and neatly lobbed the oncoming Konstantopoulos from just inside the box to give his side all three points in the 90th minute.