The Foxes also had to play over an hour of the game with ten men because of Matt Mills's sending off.
They were a man and a goal down after half an hour when centre-back Mills saw red. Referee Simon Hooper adjudged that the Foxes' centre back had been the last man when he hauled down Aaron McLean in the box. In-form forward Matty Fryatt converted the resulting penalty.
Despite the numerical disadvantage, Leicester came back into the game and levelled four minutes before the break.
Full-back Paul Konchesky finished off a quick counter-attack by cutting inside and finishing low with his weaker right foot.
Slovenian Koren won the game with two minutes left on the clock, curling an effort home from just outside the area.
Hull edge closer to the playoff spots and are now eighth, while Leicester drop out of the top six to ninth.