Having won only one of their last six league games, Leicester needed a victory to get back on track in their bid to secure a berth in next season's Champions League and they delivered with a dominant performance.
Leicester centre-back Jonny Evans stressed that the Foxes were aiming to respond to a crushing 4-1 defeat at relegation-threatened Bournemouth on Sunday and praised 19-year old debutant Luke Thomas who set up the first goal.
"It was very important, our heads dropped after the second and third goal the other day against Bournemouth, it was important we showed pride tonight," Evans told Sky Sports.
"Thomas was outstanding and everything he did was immaculate, man of the match without a doubt. He's been training really well and everyone has been really impressed with him."
The Foxes missed a string of chances to win by a bigger margin as visiting goalkeeper Dean Henderson made several reflex saves while top scorer Jamie Vardy hit the outside of the post shortly after halftime.
The defeat means Sheffield United stay eighth on 54 points, two points behind sixth-placed Wolverhampton Wanderers who occupy a Europa League qualifying spot, after their timid performance brought a four-match unbeaten run to an end.