Cort struck for the first time in six games as Wolves followed up Tuesday's 2-0 victory against Derby County with another priceless success to continue their climb up the table.
Wolves were even able to play for the final 18 minutes with ten men after Kenny Miller was sent off for collecting two yellow cards.
A last-minute strike by Rangers striker Kevin Gallen proved to be too little too late for the Loftus Road side.
But the defeat was tough on Rangers who played their part in an entertaining game played in atrocious conditions caused by heavy rain.
They had enough chances to have taken charge of the game before Cort struck.
Their failings in front of goal proved to be costly as they crashed to a second successive defeat - after a run of seven straight wins.
Wolves had to survive a number of early scares before Cort headed them in front after 22 minutes.
As early as the second minute a clearance from Colin Cameron hit Matthew Rose before bouncing back on to the post.
Gallen went close with a chip shot from fully 40 yards before a mix-up between goalkeeper Michael Oakes and central defender Mikkel Bischoff let in Martin Rowlands but he was unable to capitalise.
Having managed to ride their luck, Wolves made the decisive breakthrough thanks to the skills of winger Kevin Cooper.
He floated over a pin-point cross from the right flank that Cort headed home at the far post.
Cort almost doubled his tally six minutes later when only a last-ditch challenge by Georges Santos denied him.
Rangers had been knocked out of their stride by Cort's strike but really should have been back on level terms nine minutes before half-time.
A slip by Bischoff let in Gallen but he fired weakly at Oakes from just ten yards and his shot was easily beaten away.
Gallen was then denied by a well-timed block by Mark Kennedy on the goal-line in the 62nd minute before Cort sealed Wolves' success nine minutes later.
Cort was released by a pass from Seyi Olofinjana and raced clear of the Rangers defence before drilling his shot past Chris Day for his fourth goal of the season.
Gallen then gained some reward for his hard-working display when his 20-yard chip dropped over Oakes and into the net for Rangers' consolation strike.