Ayoze Perez gave the Foxes the lead in the 24th minute with a close-range finish but their lead only lasted for two minutes as Oliver McBurnie quickly responded with a strong header from a corner to fire the hosts back level.
Despite the lively first-half, the game lacked any real quality after the break and with it looking like the two sides would be sharing the points, Jamie Vardy ran through one-on-one to clinch the winner for Leicester in the final minute of the game and leave Chris Wilder's still side waiting for their first win of the season.
Story of the match
Foxes almost strike early on
It took nine minutes of action before a first sight of goal for either side, but it was Leicester who went closest first.
A nice ball into Perez from James Maddison saw the Spaniard find space to drive with the ball towards the Sheffield United box before slipping the ball through to Jamie Vardy.
The 33-year-old then unleashed a fierce effort which cannoned off Aaron Ramsdale's post and then cleared away to safety by the Blades backline.
Perez breaks deadlock but blades bounce back quickly.
Leicester had been in the ascendancy for the majority of the game and their dominance paid off in the 24th minute through Perez.
Making his first league start for the Foxes since October, the 27-year-old was there to pounce on Marc Albrighton's ricocheted effort and tucked the ball home to score his first goal of the season.
Despite Leicester looking in control, Sheffield United weren't behind for long however as striker McBurnie soon equalised for the hosts.
Corners have been a problem for Brendan Rodgers' side this season and once again they proved to be an issue as the Scotland international rose highest from John Lundstram's corner less than five minutes later to level the game.
Maddison goes close before the break
With the game evenly poised on the verge of half-time, Leicester came close to going back in-front - this time through James Maddison.
Perez, who had been a key figure in most of Leicester's attacking play, once again had space to run towards the Sheffield box.
Opting against shooting himself, he then laid the ball off to the onrushing Maddison, who after composing himself, unleashed a well-hit shot which was inches away from going in, instead hitting the same post that denied Vardy earlier in the game.
Vintage Vardy secures late winner
With the game lacking any sign of real quality, the game looked certain to be heading for a draw until the final moments of normal time when Vardy struck for the Foxes.
After trying to find a winner of their own, the Blades were caught napping as they held a high-line which Maddison was able to exploit as his threaded through-ball found Leicester's number nine.
Running through on goal, there was only going to be one outcome and with all the time in the world, Vardy picked his spot and curled his shot into the bottom right-hand corner of the net to give Leicester the win and move them up to third.
Set-Pieces an issue once again
It's becoming more and more of a frequent occurrence now but once again, Leicester conceded from a set-piece.
McBurnie's header to equalise in the first-half was the seventh goal the Foxes have conceded from a corner or free-kick - the highest number in the top flight.
The use of zonal marking to defend seems to be one that hasn't worked as efficiently of late and a method that Leicester boss Rodgers may have to reconsider in order to stop his side conceding so many goals.
Perez proves a point
Perez's name on the starting XI sheet was a surprise to many, but the 27-year-old certainly took advantage of his opportunity.
Playing centrally in the 3-4-1-2 formation, Perez was making his first start in the top-flight since the defeat to Aston Villa and was the key figure in many of the Leicester's attacks.
In the right place at the right time, the Foxes forward was able to finish from close-range to give Leicester the lead in Yorkshire and his ability to run into the channels, as well as collect the ball from deep and drive forward proved to be a valuable asset for his side.
His performance was one of the stand-out displays and he will have done himself no harm at the prospect of forcing his way back into the first team.
Vardy proves his worth again
As far as games go, it was one of Jamie Vardy's quieter ones, but nonetheless, the 33-year-old had the last say to give his side the win.
For the most part, Sheffield United had defended deeply, denying Vardy the space he thrives on, but as they pushed up to look for a winner, so did their defensive line and the Foxes talisman took advantage.
His winner, a cool and calm finish, stopped Leicester's run of four games without a win prior and now means that Vardy is the second top scorer in the league, behind only Dominic Calvert-Lewin and will provide Leicester with a big boost ahead of their busy Christmas fixture schedule.