Iain Hume put the Foxes ahead when he lashed home on-loan Arsenal winger Ryan Smith's cross before setting up Smith for Leicester's second minutes later.
Steve Kabba put the Blades back into the match with his strike after 52 minutes but Elvis Hammond's drive restored Leicester's lead.
Sheffield United boss Neil Warnock:
"It has been an important lesson to us because nobody has given us such an examination as they did in the first 45 minutes.
"Their front four were terrific, absolutely superb and you can't take anything away from them.
"The third goal was the sucker punch and there was no way back from that."
Leicester: Douglas, Maybury, McCarthy, Gerrbrand, Johansson, Sylla, Gudjonsson, Kisnorbo, Smith (Hamill 77), Hume, Hammond (de Vries 83).
Subs Not Used: Williams, Stearman, Tiatto.
Booked: Sylla, Gudjonsson, Maybury, Hume, Smith.
Goals: Hume 12, Smith 15, Hammond 74, Hume 90.
Sheff Utd: Kenny, Geary, Jagielka, Bromby, Wright, Gillespie (Kabba 45), Tonge (Short 85), Montgomery, Quinn, Webber, Pericard (Shipperley 70).
Subs Not Used: Ifill, Nalis.
Booked: Geary, Tonge, Montgomery, Webber, Wright.
Goals: Kabba 52, Webber 90.
Referee: K Stroud (Dorset).