Vardy, who took great delight in scoring in this fixture last season when the Foxes also won 2-1, kept his cool when through one-on-one and beat goalkeeper Aaron Ramsdale with a confident right-foot finish.
It gave Brendan Rodgers’ side a first victory in five games in all competitions and a first in three Premier League matches, moving them to within a point of leaders Chelsea.
For the Blades, it was more misery. Chris Wilder’s side have made the worst ever start to a Premier League season and remain rooted to the bottom of the table with only one point from 11 matches.
You could argue it was what Leicester deserved, having dominated possession at Bramall Lane, particularly in the first half when both Vardy and James Maddison struck the same post.
In between those efforts, Ayoze Perez marked his first Premier League start since October 18 with the opening goal, before Oli McBurnie immediately equalised with what was his first goal of the season.
There was plenty of energy from the Blades early on but it was Leicester who began to dominate possession and the hosts survived a scare after 10 minutes when Vardy unleashed a fierce strike from the right side of the area that thumped against the inside of the near post.
A better first touch from Oliver Burke midway through the first half would have seen him through on goal, after good build-up play between McBurnie and Sander Berge, but Foxes keeper Kasper Schmeichel was able to race out and smother the danger.
The home side could have been ahead, but shortly afterwards they fell behind. It is such fine margins that are not going for Wilder’s team so far this season.
A deep cross to the far post found Marc Albrighton but his shot was blocked and the ball ricocheted into the path of Perez, who rifled a shot that Ramsdale could only push into the roof of the net.
However, the Blades hit back immediately. Leicester have been vulnerable defending set pieces this season and it proved the case once more.
John Lundstram hung his cross from a corner towards the far post and McBurnie, from almost a standing start, showed good strength and determination to get above Youri Tielemans and head the ball into the bottom corner of the net.
McBurnie has been the subject of much criticism recently for his failure to score for both club and country and breaking his duck for the campaign will be a huge weight lifted off the shoulders of the Scotland international.
United understandably now had their tails up but they were unable to really capitalise on their quick response and the pattern of play slipped back to Leicester dominating the ball.
The Foxes almost made their superiority count again in stoppage time at the end of the first half but Maddison appeared to hit virtually the same spot on the post as Vardy had.
The controlled possession that Leicester enjoyed for much of the first half was lacking after the break, and that was credit to Sheffield United’s work-rate.
Wilder’s side were more of a threat in the second half and McBurnie went close again with a looping header.
The better chances were still being created by Leicester, however. Tielemans was denied by a superb recovery save by Ramsdale, who did just enough to deflect his effort over the crossbar after initially presenting the Belgium international with the opportunity after letting a cross slip through his hands.
The game looked to be heading for a draw, with the Blades on course for their second point of the season, but a loose pass in midfield from John Fleck ricocheted off of Maddison’s leg and put Vardy through on goal.
The striker raced clear and made no mistake with his finish, curling his shot around Ramsdale to win the match, leaving Wilder down on his haunches in the technical area with his head in his hands.