Jamie Ward scored with his first touch as Sheffield United blew QPR away with two goals in two minutes to book an FA Cup fourth-round meeting with Bolton.
A tight game was only separated by Lee Williamson's early effort before Ward came on with 22 minutes left and put the result beyond doubt by scoring within seconds and then, virtually from the kick-off, crossing for Richard Cresswell to make it three.
Akos Buzsaky and Damion Stewart pulled two goals back but it was too much for many home fans, who left in their droves in front of watching owner Flavio Briatore.
Yet the hosts had started brightly as former Blade Mikele Leigertwood shot just wide after 90 seconds, before Alejandro Faurlin tested Mark Bunn with a low drive.
QPR were well on top, yet as is the habit with sides low on confidence, they blew all that promise by conceding.
There appeared little on when Nick Montgomery got the ball just outside the area, but the striker floated a perfect pass in to Williamson, who drove low into the far corner for his second goal for the club.
The goal knocked the stuffing out of Rangers, although Buzsaky - the man at the centre of the controversy that saw former manager Jim Magilton leave the club last month - nearly levelled after a fine run past three players.
But amazingly the visitors could have been two ahead after having a grand total of just two shots as Ched Evans was given the freedom of the QPR half to run on to James Harper's through-ball only to fluff his lines and strike the bar.
And the home fans began to turn on their team as the second half continued, with the visitors regularly pinning them back in their own half.
Faurlin went close with a drive, yet QPR's midfield simply didn't have the guile to haul their team back into the contest.
And their mood was hardly improved when the visitors scored two in two minutes to put the game out of sight and Ward was at the heart of it.
The midfielder had been on the pitch a matter of seconds when Cresswell broke down the wing and crossed the ball directly into his path and Ward made no mistake, although Radek Cerny should perhaps have done better.
Yet there was nothing the keeper could do when Ward got free directly from the kick-off and returned the favour to Cresswell, leaving the home fans chanting 'you don't know what you're doing' at manager Paul Hart in what was just his fifth game in charge.
There was an instant response by the hosts as Buzsaky lashed home a penalty after a rather debatable handball was given against Derek Geary, before Stewart met the midfielder's free-kick to halve the deficit with just three minutes to go.
But in truth it was a case of too little, too late for the hosts as Sheffield United go marching on.