Cort opened the scoring early on with a cool volley after good work from Leon Clarke and the lively Rohan Ricketts.
But Rangers levelled moments later, Stefan Moore's left-wing cross headed down and into the net by Kevin Gallen.
Cort put Wolves ahead with a tap-in from Kenny Miller's fine centre and completed his treble in stoppage time by slotting the ball past Simon Royce.
QPR manager Ian Holloway:
"We have also conceded nine goals in three away games and we just let Cort run through us at times.
"I'm proud with how far we have come but it doesn't look quite far enough at
"We look a little bit short. We have had injuries and they may have
taken their toll."
Wolverhampton: Oakes, McNamara, Lescott, Edwards, Naylor, Anderton (Ndah 80), Ricketts, Kennedy, Miller, Cort, Clarke (Olofinjana 62).
Subs Not Used: Gyepes, Ikeme, Davies.
Goals: Cort 8, 24, 90.
QPR: Royce, Bignot, Evatt, Shittu, Milanese, Doherty (Ainsworth 76), Bircham (Bean 76), Santos, Gallen, Moore, Furlong.
Subs Not Used: Cole, Brown, Shimmin.
Goals: Gallen 12.
Ref: N Miller (Co Durham).