Andy Gray's third goal of the season was enough to give Sheffield United their third Championship win in a row.
Gray's goal came on 17 minutes, finishing from close range after being set up by Jon Harley after some hesitant QPR defending.
QPR, yet to win at home this season, saw Marcus Bean and Jamie Cureton miss good chances to level before half-time.
Lee Cook then saw a deflected shot hit the United bar, and Marc Bircham sent a shot wide as QPR pressed late on.
QPR boss Ian Holloway:
"I thought we played some decent, exciting football and should have been in front. I'm disgusted with their goal. We missed a simple header.
"I was disappointed with the second half. I was expecting us to roar at them and it wasn't a roar it was a whimper.
"We never put them under enough pressure."
Sheffield United boss Neil Warnock:
"I'm proud of them. QPR tonight would have beaten most teams. They were flying and buzzing, and will be disappointed.
"But we were disciplined and well-organised, and for all their play I didn't think they had a real opportunity.
"I think we could have finished the game off with a second goal but because we didn't we were holding on."
QPR: Day, Bignot, Edghill (Rose 64), Santos, Padula, Rowlands, Bean (McLeod 63), Johnson (Bircham 63), Cook, Gallen, Cureton.
Subs Not Used: Hamilton, Cole.
Sheff Utd: Kenny, Bromby, Morgan, Jagielka, Wright, Quinn (Francis 85), Thirlwell, Tonge (Montgomery 74), Harley, Gray (Lester 65), Ward.
Subs Not Used: Forte, Barnes.
Booked: Thirlwell.
Goals: Gray 17.
Att: 13,804
Ref: G Hegley (Hertfordshire).