Captain James McClean and Ryan Longman both had decent efforts early on as Wrexham carried the greater threat without overly troubling QPR goalkeeper Paul Nardi – who was making his first league start of the season.
The Rs improved though and saw Koki Saito fire straight at Arthur Okonkwo, before skipper Jimmy Dunne rifled beyond Okonkwo from close range after Wrexham failed to clear from a corner – although the effort was ruled out for offside.
But the visitors got their rewards in the 33rd minute as Wrexham again failed to clear their lines, and Burrell’s poked effort was saved by Okonkwo, only to rebound into his own net off the legs of the unfortunate Coady.
Kone and Burrell both had efforts to extend the away side’s lead either side of Ryan Hardie’s effort as the home supporters grew frustrated.
And QPR did double their lead before the break as they carved through the Wrexham defence, before Kone’s drilled effort flew into the net via the underside of the crossbar.
A swift improvement was needed by the hosts and they were firmly on top after the restart, although Okonkwo still had to be alert to keep out Jonathan Varane’s curling shot.
Hardie, McClean and substitute Sam Smith were among those to go close, but Wrexham did bulge the net as Moore headed Lewis O’Brien’s corner beyond Nardi to score in a third consecutive league match for the first time since 2022.
Ryan Longman’s goal-bound header was then blocked as Phil Parkinson’s men pushed, but they were undone on the counter as Burrell chipped over Okonkwo – with Karamoko Dembele hitting the post late on – as Julien Stephan’s side earned a second successive win.