Sharp scored a stunning early volley to open the scores in only the second minute, and then fired the winner from the penalty spot after Pierre-Michel Lasogga had earlier dragged Leeds level with a header minutes into the second half.
“We needed the win,” Blades boss Chris Wilder, whose side failed to score in defeats to Aston Villa and Wolves in their last two games, said afterwards.
“I’m sick of banging on about how well we’re playing and not getting results. People are looking at me as if I’m a bit of a nutter, going on about it.
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“We were close against Villa but we didn’t deserve anything against Wolves.
“We’re at the business end of the season and we need to pick wins up. We’ve got one and we’re off and running.”