Ayoze Perez’s strike and an own-goal from Ethan Ampadu also helped Leicester return to second place in the standings, ahead of Manchester United’s game against West Ham later.
It rounded off a difficult week for Sheffield United which had seen the departure of manager Chris Wilder, with youth coach Paul Heckingbottom in temporary charge.
It was the same old story for the Blades, as they struggled to make an impression or trouble Leicester as an attacking threat.
Jamie Vardy dragged a 20-yard shot wide after eight minutes before Perez’s glancing header was touched on to the post by Sheffield United goalkeeper Aaron Ramsdale shortly afterward. Ramsdale then blocked a low shot from Vardy with his legs.
Leicester made the breakthrough six minutes before halftime. Some sharp, incisive passing between Youri Tielemans and Perez resulted in Vardy getting in behind the defense down the left-hand side. His low cross left Iheanacho with a simple tap-in from close range.
Five minutes into the second half, Iheanacho tried to return the favor for Vardy but he saw his effort brilliantly headed off the line by Chris Basham.
Iheanacho then put Vardy through on goal after an hour but once again Ramsdale denied the striker with his legs.
A second goal was coming and Leicester doubled its lead in the 64th. Marc Albrighton led a counterattack and teed up Perez who found the bottom corner with a strike from the edge of the penalty area.
Vardy was the provider for Iheanacho five minutes later, with the striker guiding the ball past Ramsdale from 12 yards.
Iheanacho completed his treble in the 78th, driving a low shot from 25 yards beyond Ramsdale and into the bottom corner of the net.
It got worse for the visitors two minutes later when Vardy’s shot from the left side of the penalty area, which looked to be heading wide, ended up in the back of the net via the outstretched leg of Ampadu.
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