A single solitary goal by striker Danny Webber was enough to ensure their first ever victory at the Walkers Stadium, and despite their below mid-table position put them just six points behind the last Play-Off place.
The Foxes have claimed just one league victory at the Walkers Stadium this season; a 4-1 victory over Watford but was unable to add to that tally when Danny Webber turned in on-loan defender Phil Barrdsley's cross in the second half of the game.
The home side did get their chances and there first chance arrived as little as the fourth minute when Alan Sheehan shot 20 yards past Paddy Kenny's left hand post.
However it wasn't until near half-hour mark when United pushed forward for their first assault on goal when Bardsley struck from 20 yards also but saw his effort turned away by Marton Fulop with Gary Cahill heading over the top following Keith Gillespie's corner kick.
City skipper Stephen Clemence was forced to be substituted after only 18 minutes through injury and was replaced by Shaun Newton; and on 32nd minute Collins John replaced Dudley Campbell.
Blades keeper Paddy Kenny also joined the injury list when he hobbled off with a leg injury after clattering with his own defender Gary Cahill.
After the break both sides quickened the pace as each side saw the potential of three points on the cards, but United got in the first opportunity when Bardsley drove his 22 yard effort at Fulop.
Leicester City this season have boasted a decent defensive record and consider themselves to have the tightest defence in the Championship this season with on 8 goals shipped past them in ten league games; but there defence was breached by Webber.
On 55 minute the Blades were rewarded with their persistence when the ever so busy Bardsley whipped in a cross from the right only to see it land to the feet of Danny Webber to slide in turn home at the near post.
Levi Porter was brought in, in place of Bruno N'Gotty as Gary Megson switched to a traditional 4-4-2 formation but United didn't sit back and relax and almost doubled there lead when James Beattie out smarted Patrick Kisnorbo to chip over the top before Cahill headed over Gillespie's free-kick.
And United once again struck the back of the net when a well antiquated move saw Beattie handed the simple task of heading home at close range following a short cross from Webber, but Beattie wasn't to net his tenth goal of the season when his goal was ruled out for offside.
Disappointed Foxes fans chanted for 'Megson for Bolton' just nine games into his City reign as Bryan Robson escaped the 'Robson Out' chanting when eluded him following the 1-1 draw with Preston North End the previous Saturday.
The Blades move to 17th in the table with 13 points from twelve games; just four points clear of rivals Sheffield Wednesday who occupy that last relegation place after there 2-1 home defeat to Scunthorpe United.