Sheffield United manager Chris Wilder left the club late on Saturday and coach Paul Heckingbottom, who will take charge until the end of the season, had no time to fix the team’s defensive frailty and toothless attack.
Leicester went ahead in the 39th minute when Jamie Vardy latched on to a clever pass and his perfect centre left Iheanacho with the simple tap-in.
Ayoze Perez added the second in the 64th minute with a low shot, Vardy again assisted Iheanacho for another simple finish and he saved the best for last, firing home a powerful left-foot shot in the 78th minute to complete his first Premier League hat trick.
A Vardy shot was turned into his own net by Ethan Ampadu to complete the rout as Leicester climbed up to second spot on 56 points after 29 games, two ahead of Manchester United who play West Ham United later on Sunday.
Sheffield United remained bottom on 14 points, 14 behind Newcastle United in 17th place.