Ollie Norwood scored the main objective on nine minutes to hand QPR their 6th loss in seven association games - and a fourth in succession.
John Fleck's corner was dummied, permitting midfielder Norwood to track down the base right corner from 18 yards - his first objective in more than two years. He last scored in a 2-0 FA Cup succeed at Millwall in January 2020.
The hosts, who are currently unbeaten in 11 home association games, of which they have won eight, might have fixed triumph by a more extensive room for error.
Star turn Morgan Gibbs-White drifted a sharp right-foot chip simply finished and whistled a low right-foot shot only wide subsequent to being sent clear by John Fleck.
Yet, QPR squandered a decent late possibility when Elias Chair controlled a free-kick that was impeded by the divider - and Lyndon Dykes headed wide in the fifth moment of added time.
Paul Heckingbottom's Blades presently lie fifth, the third best positioned in the scrum of six clubs isolated exclusively by five.
Mark Warburton's Hoops have dropped to 10th, presently three focuses short of a play-off place.
The two clubs have six games left, including the return apparatus when QPR have the Blades on the penultimate Saturday of the period.
In any case, before then, this Saturday, the Blades have second-put Bournemouth at noon, trailed by QPR's outing to Preston.
Edges supervisor Paul Heckingbottom told BBC Radio Sheffield:
"The objective was from a set-piece schedule that we've utilized previously and getting an objective from it was extraordinary.
"We'd addressed any outstanding concerns or issues on it. Ollie Norwood and John Fleck changed their schedules a piece as we most likely were aware they'd have their home work on us.
"Ollie was great. Each player has various properties and he has a few outstanding ones. He restarted ownership, won a great deal of second balls and got the champ as well.
"Yet, when there's just a single objective in it, you never feel great and we realized we'd need to remain steadfast eventually."
QPR supervisor Mark Warburton told BBC Radio London:
"We never tried their manager in the manner we needed. What's more, we surrendered a terrible put forth piece objective.
"The last part was greatly improved however we coming up short on piece of trickiness you want to open them up.
"They're efficient with an impressive home record we've actually got to play these young men once more.
"However, there's as yet 18 focuses on the table. Everybody will drop focuses and take focuses off one another. We need to stay together and get ready for Preston on Saturday."
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