Sam Clucas scored against his boyhood club to put the visitors ahead early on but Christian Fuchs levelled before the break.
Riyad Mahrez put Leicester in front 15 minutes into the second half after forcing Eldin Jakupovic into an error from the edge of the box.
And an own goal from Tom Huddlestone compounded Hull's misery at the death.
Leicester began the game with the same renewed vigour they showed in defeating Liverpool - the first match since Ranieri was sacked - and created a host of early chances.
Wes Morgan headed wide from a Mahrez free-kick before two dangerous low crosses from Jamie Vardy into the six-yard box were expertly turned behind under considerable pressure by Harry Maguire and then Andrew Robertson.
Maguire then bravely threw himself in front of a goal bound shot from Robert Huth and Hull survived once more.
It was against the run of play when Hull took the lead after 14 minutes.
Clucas led a swift break through the middle before Oumar Niasse and Kamil Grosicki combined down the left side of the penalty area and Clucas, released by Leicester as a schoolboy, slid in to poke home Grosicki's cross from six yards out.
Not for the first time since Ranieri's sacking, the Leicester players were under the spotlight and asked to respond - and as against Liverpool they did so.
Left-back Fuchs linked up brilliantly with Vardy down the flank, playing a couple of one-twos before continuing his run into the area where he was on hand to finish off Vardy's cut back from 10 yards out. However, goalkeeper Eldin Jakupovic will be disappointed the ball crept beneath him.
Having frustrated Leicester at one end during the first half, Maguire made a nuisance of himself in attack at the start of the second.
The defender saw a header clip a post following a corner and shortly afterwards worked Kasper Schmeichel with another header from a Grosicki delivery.
Jakupovic kept out a tame effort from Mahrez just before the hour, but the Algeria international was merely finding his range.
Next time the ball was at his feet, Mahrez turned Robertson one way then the other trying to create an opening for a shot and, after cutting back for the third time, he found the bottom corner with a shot from the edge of the area.
It was a rare glimpse of the magic that earned him the PFA Players' Player of the Year award last season, but once more Jakupovic should probably have done better.
Hull tried to respond immediately and Schmeichel had to punch clear a free-kick whipped in by Grosicki before blocking an effort from Niasse at his near post with six minutes remaining.
After Jakupovic saved to deny Demarai Gray, Leicester sealed victory in the final minute when Onyinye Ndidi's header from a corner struck Huddlestone and flew into the net.
It was a huge win for the champions, who are now five points clear of the relegation zone.
Hull, meanwhile, remain second bottom of the table and are four points from safety after Crystal Palace won at West Brom.