Sheffield United were knocked off the top of the Championship as QPR took full advantage of an early mistake by Blades goalkeeper Jamal Blackman.
Idrissa Sylla swept in the only goal into an open net after Blackman collided with team-mate Cameron Carter-Vickers trying to gather a high ball.
Blackman played no further part in the match because of a head injury.
Sheffield United were unable to force an equaliser to prevent a first defeat in four games and slipped to third.
Chris Wilder’s side were replaced by Wolves, the team QPR beat at home on Saturday, at the Championship summit.
Having gone seven games without a win before that, the Hoops have now recorded back-to-back victories to move up to 12th.
Victory could have been more emphatic for Ian Holloway’s side had Sylla been able to head home dangerous crosses from Conor Washington and Luke Freeman in either half.
Sylla’s replacement, Jamie Mackie, also spurned a glorious chance when he fired over from just 10 yards out after Freeman’s clever through ball.
Leon Clarke went closest for Sheffield United to breaking the deadlock but Alex Smithies was able to smother his close-range effort on the stroke of half-time from Enda Stevens’ low cross.
Clarke also had a goal disallowed in the second half as Billy Sharp strayed offside.
QPR manager Ian Holloway:
“That is a fantastic team we played against. We got a very lucky goal but we forced that – we put three up front and wanted to see how they could deal with what we’ve got.
“It was a big win and we needed it. We had a big win as well against Wolves on Saturday and now let’s see if we can get that first away win.
“It feels great. It’s so important to find that buzz and the fans are starting to trust their team.”
Sheffield United boss Chris Wilder:
“Our start wasn’t the greatest, with the injury to Jamal and the goal, but I just didn’t think we deserved anything.
“I’m disappointed with my team. We’ve been out-fought and out-battled and didn’t show enough quality.
“We knew that they were going to press and get at us and we needed to show composure, but we didn’t.
“We were also sloppy in the second half of the game. It’s not been a good night and ended in a deserved defeat.”