The Blades responded well to Saturday’s setback at Stoke City, which saw them drop to eighth, as Ollie Norwood scored a first-half winner against another play-off chasing side in QPR.
Paul Heckingbottom’s side were good value for their lead, but Rangers came into the game as the first half wore on and began to create more opportunities. But goalkeeper Wes Foderingham ended the game without a proper save to make as United picked up another three points at home.
They return to Bramall Lane this weekend to face second-placed Bournemouth, with four of their remaining six games at home.
But the victory came at a cost, with new boy Filip Uremovic limping out of the game around the hour mark with what looked to be a knee complaint.
1. Wes Foderingham 6
Had an easier time of things than his opposite number Westwood, who was heckled throughout the second half by the Kop who didn't let him forget his previous connections with the other side of Sheffield. Stood up to some late pressure well at the end Photo: Andrew Yates
2. George Baldock 7
Played his part in Norwood's opener as he dummied the corner kick and saw the midfielder score from the edge of the box. Played his part in a good defensive rearguard action after that Photo: Richard Seller
3. Filip Uremovic 7
Received a warm welcome as his name was read out ahead of kick-off and looked very impressive on his debut - until he was hit by the Blades defensive curse and picked up an injury about an hour in, being replaced by Robinson Photo: Richard Seller
4. John Egan 8
Almost turned provider with an excellent through-ball intended for Gibbs-White, who was only prevented from bearing down on Westwood's goal by a well-timed tackle from Wallace. Defensively so solid, including a brave headed clearance from Chair's well-struck free-kick Photo: Isaac Parkin