The Premier League champions beat Liverpool by the same scoreline on Monday in their first game since the controversial sacking of Ranieri.
Yet they seemed set to come back down to earth after 14 minutes on Saturday, Sam Clucas' close-range effort putting Hull ahead.
However, the two stars of Leicester's incredible title-winning campaign under Ranieri had a hand in what could prove to be a crucial comeback.
First, Jamie Vardy set up Christian Fuchs to level the scores midway through the first half.
Riyad Mahrez then completed the turnaround just before the hour mark when he hit home from the edge of the box, with a late Tom Huddlestone own-goal adding gloss to the scoreline as Leicester made it two wins from two under caretaker Craig Shakespeare and leaving Hull second bottom - four points adrift of safety.
Wes Morgan wasted a superb opportunity to open the scoring inside five minutes, heading wide unmarked from a Mahrez free-kick.
Leicester continued to enjoy the better of the opening stages but, amid a sustained period of pressure, the hosts were caught on the counter.
Wilfred Ndidi carelessly gave the ball away and Hull ruthlessly took advantage, Oumar Niasse slipping in Kamil Grosicki, whose cross from the left was turned in by Clucas after Kasper Schmeichel could only push it into the midfielder's path.
But Leicester responded 13 minutes later as Fuchs and Vardy linked up superbly down the left before the England international found the Austrian arriving late into the box to tuck the ball home.
Hull were denied by the woodwork shortly after the restart, Harry Maguire striking the post with an improvised effort off the bottom of his boot from Grosicki's corner.
However, that was a fleeting moment of promise for Hull and Leicester continued to push for a turnaround, which they did through a moment of Mahrez magic.
The Algeria winger danced on the edge of the area as he searched for space before squeaking a fierce low effort inside the right-hand post, with Eldin Jakupovic not able to keep the shot out despite getting a hand to it.
Schmeichel had to be alert shortly after to keep out Grosicki's free-kick from a difficult angle.
Hull rarely threatened after that missed opportunity, though, and Huddlestone inadvertently headed a corner into his own net late on to make it 3-1, with Leicester's Thai owners pictured giving the thumbs up at the end of Shakespeare's latest audition for the job.