Nedum Onuoha scrambled home a fourth-minute opener as an early corner caused havoc for the Leeds defence and had goalkeeper Rob Green in trouble against his former side.
QPR doubled their lead through Tjaronn Chery’s 73rd-minute penalty, awarded after full debutant Ronaldo Vieira tangled with Jordan Cousins.
And a miserable afternoon for Leeds got even worse in the final minute of stoppage time when a clinical finish from Sebastian Polter left Leeds bottom of the division on goal difference.
United rarely threatened Alex Smithies in the QPR goal, and the Hoops also hit the post twice.
As was so often the case last season, United lacked a cutting edge, with the Whites forced to play without new signing Pablo Hernandez, who has yet to receive international clearance for his move from Al-Arabi.
In bright London sunshine, United got off to the worst possible start when the hosts scrambled home a fourth-minute opener from Chery’s corner, which caused bedlam in the Leeds box.
An initial half-volley from Steven Caulker was blocked, but the ball eventually looped over the line through a combination of the presence of Onuoha, Sol Bamba and an under pressure Green who failed to clear against his former side. The Hoops immediately had their tails up and continued to dominate with Onuoha blazing over.
Leeds then lost the returning Gaetano Berardi to injury as Lewie Coyle was called on after just 22 minutes.
QPR continued in the ascendancy and the hosts were then denied by the same post twice in 10 minutes.
First a clearance from Vieira cannoned into the leg of Chery and back onto Green’s left-hand post. Then a clinical QPR counter-attack led to Polter turning Bamba in the area and firing a low effort that hit the same piece of woodwork.
United’s only slight chance fell to Kemar Roofe, who headed wide, and the half ended with Charlie Taylor blazing wildly over the bar.
Leeds briefly offered hope after the break when Matt Grimes curled a long-range free-kick over the bar, but that proved a false dawn and the introduction of Hoops substitute Abdenasser El Khayati caused chaos.
QPR immediately forced two smart saves from Green, the first from a tight angle to deny Chery and the second seeing the veteran tip away El Khayati’s curled effort that was heading into the bottom-right corner.
But just one minute later Green was again picking the ball out of his net after Chery converted a 73rd-minute penalty.
From an attack down the right flank, Vieira got in a tangle with Cousins and clumsily brought down the Hoops player for what looked like a stone-wall penalty.
Chery coolly slotted the ball home into the bottom right corner to double the Hoops’ lead and United’s afternoon was summed up by a glaring miss from substitute Marcus Antonsson, who was presented with a one-on-one by a stray back pass but rolled the ball a yard wide.
Fellow substitute Hadi Sacko then finally found the net for United, but his effort was chalked off for handball, after which Coyle picked out Antonsson, who fired just over. The striker again held his head in frustration. It was that sort of day.
To top it all, QPR then bagged a demoralising third goal in the fifth minute of stoppage time when Polter waltzed into United’s area and produced a stunning finish to fire across Green into the right corner.
United were finally put out of their misery soon after by the full-time whistle, with the Leeds players then making their way to applaud the 3,200 travelling Whites fans for their support in the way end. The response from United’s travelling contingent was not pleasant – rather like the efforts of the team for which they had woken up early and paid good money to support.
Leeds United: Green, Berardi (Coyle 22), Bamba, Bartley, Taylor, Diagouraga, Vieira, Grimes (Antonsson 61), Dallas, Roofe (Sacko 75), Wood. Subs not used: Turnbull, Cooper, Phillips, Mowatt.
QPR: Smithies; Bidwell, Hall, Onuoha, Chery (Perch 88), Gladwin (Cousins 56), Polter, Henry, Luongo, Caulker, Shodipo (El-Khayati 68). Subs not used: Ingram, Lynch, Washington, Kpekawa.
Referee: Oliver Langford.
Attendance: 16,764 (3,213 Leeds).