In the opening moments Danny Webber flashed a header just wide but City went closer on five minutes when Nils-Eric Johansson nodded Momo Sylla's deep corner back across the face of goal for Elvis Hammond to crash a header against the bar.
City had the upper hand, but it was United who almost snatched the lead when hesitancy in the home defence let in Webber who drove an angled shot straight at Rab Douglas.
Leicester looked eager to press forward at every opportunity and their enterprise was rewarded after 11 minutes when recalled striker Iain Hume gave them the lead.
Ryan Smith's cross from the right was headed down by Hammond for Hume to smash an unstoppable half volley from five yards beyond Paddy Kenny.
Things got a whole lot worse for Neil Warnock's men on 15 minutes when Hume turned provider crossing from the right after a good run for Smith to guide a simple header beyond the keeper from close range.
The visitors continued to be unsettled by City's high tempo game and they almost fell three behind when Alan Maybury's 20-yard drive took a deflection before rolling inches wide of the far post.
Steve Kabba was a half-time substitute for Keith Gillespie and within six minutes of the restart he had pulled a goal back for United.
Michael Tonge found Webber who crossed low into the six-yard area for Kabba to slide the ball home.
Hammond soon had a chance to restore the Foxes' two-goal advantage when he raced clear but Kenny was quickly off his line to save bravely with his feet.
On the hour mark Douglas kept City ahead when he clawed away Derek Geary's goalbound angled drive.
But Leicester continued to look dangerous on the break and Hammond squandered a wonderful opportunity to ease the pressure on his team-mates when from close in he shot against the keeper's legs after good work by Sylla and Joey Gudjonsson.
But there was no denying Hammond on 74 minutes when clever footwork by Smith unhinged the Sheffield rearguard allowing the City striker to drill home from seven yards.
Hammond was having his best ever game for City since signing for £350,000 from Fulham in the summer and he almost breached United again with a 16-yard drive towards the near post which Kenny was grateful to scramble away for a corner.
Three minutes from the end Webber's intended cross bounced off the bar but confident Leicester remained in control.
The win was sealed in time added on when substitute Joe Hammell stole the ball from a dithering defender to feed Hume, who surged into the penalty area before smashing a drive beyond the keeper.
At the death Craig Short nodded home Alan Quinn's corner, but it was never enough to take the gloss off a polished Leicester performance.