New signing Gary Madine and fellow loan arrival Kieran Dowell were named on the bench by Blades manager Chris Wilder.
And the Blades could have been in front after just four minutes. A long diagonal ball picked out Billy Sharp, who unselfishly played in David McGoldrick, but the striker could not keep his effort on target.
But McGoldrick was on target on 37 minutes in a move he started and finished. The striker could have let a ball go for a throw-in, but kept it alive, before a lovely cross-field pass.
Ollie Norwood's excellent cross then returned the ball to McGoldrick, who powered his header beyond Joe Lumley.
Rangers - who before the goal had tried to slow the game down and waste time - suddenly picked up the pace, Ebere Eze testing Dean Henderson with a deflected shot from 40 yards out.
Chances were at a premium in the second half, with the visitors looking to play on the counter attack.
Enda Stevens dragged an effort wide for United - who brought on Dowell and Leon Clarke in the second half in search of a second goal - while Luke Freeman was off target with his long-range effort for QPR.
Wilder felt it was the right result and well deserved.
McGoldrick’s tenth goal of the season was enough for United to take all three points and move up into the automatic promotion places.
Wilder said: “It is job done, it was a tough game. They were on a good run of form, no result is given to you in the Championship and you have to work extremely hard to do things right.
“Given the run they’re on, it is well deserved. We’ve had to overcome stubborn and difficult opposition today but I think the right result is the one that has happened.
“We always talk about that it’s not going to be free-flowing and we’re not going to create chance after chance, but it is football and we’ve talked about that one bit of quality that we need and we’ve got it today.”
Wilder also paid tribute to match-winner McGoldrick “We’re a team on the front foot and we try and dominate the opposition and create chances. There are goals to be had for the strikers for me, but obviously they’ve got to finish them.
“It is important their overall play is good and that they do their job, but ultimately they want to get into double figures as quickly as possible so with David doing that today, it is testament the way he’s gone about his job.