The Blades were ahead inside 12 minutes from the spot.
Beattie did well to flick on a long ball for Billy Sharp, who went over under the close attentions of Patrick Kisnorbo. The defender was the last man and saw red.
Beattie’s penalty was parried by Paul Henderson, but the rebound fell for the striker who made no mistake.
Two minutes later Richard Stearman felled Sharp 20 yards from the Leicester goal.
Beattie’s free-kick bounced before it reached Henderson’s goal but the keeper should have done better.
After 17 minutes Beattie completed his hat-trick when he headed in from Michael Tonge’s corner.
Leicester’s best chance came in the second half but Matty Fryatt’s shot was saved by Ian Bennett.