England striker Vardy headed home on 66 minutes from a cross by Riyad Mahrez, who was welcome back by Leicester fans from his self-imposed 10-day exile.
Mahrez made his first home appearance since skipping training and two games in a stand-off over Leicester’s refusal to sell him to Manchester City.
A few boos for the Algerian were largely drowned out by cheers and he responded by laying on the winner for Vardy, who grew up supporting the Blades’ bitter Steel City rivals.
Leicester star Mahrez showed some more clever touches early in the second half as the Foxes worked their way slowly back on the front foot.
But their first effort on goal since half-time did not arrive until the 57th minute, when Wilfred Ndidi fired just over the crossbar from outside the box.
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Then another clever spell of passing have Vardy a chance to drive into the box but his cross-shot was blocked.
Gray’s clever turn and well-judged pass then sent Mahrez scampering down the right but his touch, for once, let him down and he ran it out for a goal-kick.
Mahrez laid on the opener on 67 minutes, however, as he twisted to shift the ball onto his left foot and delivered a cross to Vardy, who looped a header from beyond the far post over Blackman and in.
Gray almost doubled the lead with a curling shot with Blackman making a good save.
But moments later it could have been 1-1 as Schmeichel made a superb, low save to keep out a shot from George Baldock.