On-loan Stoke City striker Richard Cresswell struck in first-half stoppage time to keep Sheffield United's FA Cup hopes alive.
Queens Park Rangers proved a tough nut to crack under new manager Paul Hart, while the home side dominated for long periods but couldn't find a way past Radek Cerny.
United carved out an early opening after Derek Geary was fouled by Alejandro Faurlin, Jamie Ward's precise free-kick found centre-back Chris Morgan whose close-range header flashed wide of the left-hand upright.
The Sheffield side should have snatched the lead in the ninth minute, Henri Camara's quick feet deceiving the QPR defence as he passed unselfishly to Stephen Quinn, but from ten yards the little midfielder hammered his right-foot shot against the crossbar.
Rangers found their way blocked by a resolute United defence, Jay Simpson trying with a long-range strike, saved at the foot of the far post by the diving Mark Bunn.
Argentinian midfielder Faurlin went even closer with a fierce strike from 25 yards, Bunn was unable to hang on to the ball as it spun out of his hands and wide of the target.
Rangers' persistence paid off in the 39th minute with the United back four at fault , they failed to cut out Wayne Routledge's low cross from the right and Simpson added the finishing touch firmly sidefooting past Bunn from ten yards.
United were back on level terms in first-half stoppage time, Quinn delivering the cross as Cresswell steered his header into top left-hand corner from close range.
Camara almost added a second minutes after the re-start, drilling in a stinging right-foot shot which Cerny could only push away, before Ward saw his effort spin inches wide after neat work from Ched Evans.
Gary Borrowdale blocked Camara's shot on the turn and as United looked for a second goal, it almost came ten minutes from the end.
Evans' spectacular free-kick from all of 35 yards crashing back off the bar with Cerny well beaten.