Neil Critchley suffered defeat in his first home match in charge of QPR as Luton took the spoils at Loftus Road.
Having overseen a win at Preston in his first match, Critchley made three changes to his starting line-up after the Boxing Day stalemate at Cardiff City and saw Olamide Shodipo beat his man and get to the byline on the right, but fail to pick out a teammate in the box.
But Luton took the lead moments later as Alfie Doughty found Carlton Morris on the left edge of the box and his low shot flew through the legs of Ethan Laird and inside the far post.
Ilias Chair saw a shot comfortably saved by Ethan Horvath after a strong run from midfield on 21 minutes, with the visitors clearing a corner on the half-hour mark as QPR upped the tempo.
And Horvath pushed a long ball into the box over the crossbar just before half-time, with Jordan Clark producing two clearances as the hosts looked to profit from the set-piece.
Doughty picked up the first booking of the night before the break but the second half was barely two minutes old when Luton doubled their advantage, as Kenneth Paal headed James Bree's free-kick into the path of Morris, who tapped in at the far post.
But QPR were inches away from a reply on 54 minutes when Tyler Roberts saw his header from a free-kick come back off the crossbar.
The hosts had penalty shouts for a challenge on Laird turned down, before Lyndon Dykes had a header deflected behind by Tom Lockyer.
Chair made way for Chris Willock midway through the second half, with Luton's Clark, Dan Potts and Pelly Ruddock Mpanzu picking up further yellow cards as tempers began to fray.
Dykes fired across the face of goal when Roberts whipped a cross to the far post on 74 minutes, with Luke Freeman coming on to face his former club soon after.
Roberts and Shodipo made way for Taylor Richards and Albert Adomah, but Rangers fell 3-0 behind soon after as Doughty thumped home from the edge of the box.
Critchley's men will look to bounce back when they begin 2023 with another home match against Sheffield United on Monday (January 2, 8pm).
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